Finding equation of an ellipse given four points [closed]
I am just wondering how can I find the equation of an ellipse given that it passes through these four points?
A(1,1)
B(3,4)
C(1,7)
D(-1,4)
Appreciate any solutions and answers.
calculus geometry conic-sections
asked Dec 3 '18 at 8:47
Matthew
1
closed as off-topic by Brahadeesh, Alexander Gruber♦ Dec 4 '18 at 4:30
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Brahadeesh, Alexander Gruber
If this question can be reworded to fit the rules in the help center, please edit the question.
|
show 3 more comments
I am just wondering how can I find the equation of an ellipse given that it passes through these four points?
A(1,1)
B(3,4)
C(1,7)
D(-1,4)
Appreciate any solutions and answers.
calculus geometry conic-sections
asked Dec 3 '18 at 8:47
Matthew
1
closed as off-topic by Brahadeesh, Alexander Gruber♦ Dec 4 '18 at 4:30
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Brahadeesh, Alexander Gruber
If this question can be reworded to fit the rules in the help center, please edit the question.
Four points are generally not enough to determine an ellipse uniquely. What other constraints do you have?
– amd
Dec 3 '18 at 9:43
@amd, there are no other constraints
– Matthew
Dec 3 '18 at 9:48
1
Plot the points, it certainly looks like you can say more about this ellipse.
– Paul
Dec 3 '18 at 9:53
Perhaps the principal axes of your ellipse are meant to be parallel to the coordinate axes? Otherwise, there is an infinite number of ellipses that pass through these points.
– amd
Dec 3 '18 at 9:54
@Paul I actually can't, this question is found on a highschool textbook
– Matthew
Dec 3 '18 at 9:57
|
show 3 more comments
I am just wondering how can I find the equation of an ellipse given that it passes through these four points?
A(1,1)
B(3,4)
C(1,7)
D(-1,4)
Appreciate any solutions and answers.
calculus geometry conic-sections
asked Dec 3 '18 at 8:47
Matthew
1
I am just wondering how can I find the equation of an ellipse given that it passes through these four points?
A(1,1)
B(3,4)
C(1,7)
D(-1,4)
Appreciate any solutions and answers.
calculus geometry conic-sections
calculus geometry conic-sections
asked Dec 3 '18 at 8:47
Matthew
1
asked Dec 3 '18 at 8:47
Matthew
1
asked Dec 3 '18 at 8:47
Matthew
1
asked Dec 3 '18 at 8:47
Matthew
1
asked Dec 3 '18 at 8:47
Matthew
1
1
closed as off-topic by Brahadeesh, Alexander Gruber♦ Dec 4 '18 at 4:30
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Brahadeesh, Alexander Gruber
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Brahadeesh, Alexander Gruber♦ Dec 4 '18 at 4:30
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Brahadeesh, Alexander Gruber
If this question can be reworded to fit the rules in the help center, please edit the question.
Four points are generally not enough to determine an ellipse uniquely. What other constraints do you have?
– amd
Dec 3 '18 at 9:43
@amd, there are no other constraints
– Matthew
Dec 3 '18 at 9:48
1
Plot the points, it certainly looks like you can say more about this ellipse.
– Paul
Dec 3 '18 at 9:53
Perhaps the principal axes of your ellipse are meant to be parallel to the coordinate axes? Otherwise, there is an infinite number of ellipses that pass through these points.
– amd
Dec 3 '18 at 9:54
@Paul I actually can't, this question is found on a highschool textbook
– Matthew
Dec 3 '18 at 9:57
|
show 3 more comments
Four points are generally not enough to determine an ellipse uniquely. What other constraints do you have?
– amd
Dec 3 '18 at 9:43
@amd, there are no other constraints
– Matthew
Dec 3 '18 at 9:48
1
Plot the points, it certainly looks like you can say more about this ellipse.
– Paul
Dec 3 '18 at 9:53
Perhaps the principal axes of your ellipse are meant to be parallel to the coordinate axes? Otherwise, there is an infinite number of ellipses that pass through these points.
– amd
Dec 3 '18 at 9:54
@Paul I actually can't, this question is found on a highschool textbook
– Matthew
Dec 3 '18 at 9:57
Four points are generally not enough to determine an ellipse uniquely. What other constraints do you have?
– amd
Dec 3 '18 at 9:43
Four points are generally not enough to determine an ellipse uniquely. What other constraints do you have?
– amd
Dec 3 '18 at 9:43
@amd, there are no other constraints
– Matthew
Dec 3 '18 at 9:48
@amd, there are no other constraints
– Matthew
Dec 3 '18 at 9:48
1
1
Plot the points, it certainly looks like you can say more about this ellipse.
– Paul
Dec 3 '18 at 9:53
Plot the points, it certainly looks like you can say more about this ellipse.
– Paul
Dec 3 '18 at 9:53
Perhaps the principal axes of your ellipse are meant to be parallel to the coordinate axes? Otherwise, there is an infinite number of ellipses that pass through these points.
– amd
Dec 3 '18 at 9:54
Perhaps the principal axes of your ellipse are meant to be parallel to the coordinate axes? Otherwise, there is an infinite number of ellipses that pass through these points.
– amd
Dec 3 '18 at 9:54
@Paul I actually can't, this question is found on a highschool textbook
– Matthew
Dec 3 '18 at 9:57
@Paul I actually can't, this question is found on a highschool textbook
– Matthew
Dec 3 '18 at 9:57
|
show 3 more comments
2 Answers
2
active
oldest
votes
There are infinite ellipses determined by four points. By representing your four points the simplest option is a vertical ellipse.
In that case, first of all you must know the general equation of an ellipse
$$ Mx^2+Ny^2 +Px+Qy +R =0. $$
There are five coefficients (M, N, P, Q, and R) but your information is only four points. Assume M =1 and substitutes the values x and y for each point. You will get a linear system. Solve it and that's all.
answered Dec 3 '18 at 10:18
Antonio Luis
212
Or you can find the center and the semi-axes graphically (look at the picture).
– Antonio Luis
Dec 3 '18 at 10:20
Thanks for the solution Antonio, I am able to comprehend from your graphic solution. Turns out the four points are vertices of the ellipse, I am able to solve for the equation using the center and semi-axes.
– Matthew
Dec 3 '18 at 11:12
add a comment |
If $A,B,C$,&$D$ are the 4 vertices of this ellipse then the intersection of $AC$ and $BD$ is the center of this ellipse which is $I(1,4)$
Now $IA=3$ and $IB=2$
Thus the equation of this ellipse is $$frac{(x-1)^2}{4}+frac{(y-4)^2}{9}=1$$
answered Dec 3 '18 at 10:39
Fareed AF
44211
Appreciate the solution kind sir
– Matthew
Dec 3 '18 at 11:12
@Matthew Your much welcome :)
– Fareed AF
Dec 3 '18 at 11:14
You’ve made a tacit assumption that the ellipse is axis-aligned. The question makes no mention of that.
– amd
Dec 3 '18 at 23:52
@amd True, but as they mentioned above, to define an ellipse we need 5 points, from 4 points you can't get the equation of an ellipse unless these 4 points are the vertices. Also I started my answer with if they are the vertices ...
– Fareed AF
Dec 4 '18 at 4:28
Fair enough. However, it is untrue that you can’t get the equation of an ellipse from four points—it’s just that there’s not a unique ellipse through those points. It’s a fairly simple matter to derive the equations of a one-parameter family of ellipses that all pass through those points.
– amd
Dec 4 '18 at 5:23
|
show 1 more comment
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
There are infinite ellipses determined by four points. By representing your four points the simplest option is a vertical ellipse.
In that case, first of all you must know the general equation of an ellipse
$$ Mx^2+Ny^2 +Px+Qy +R =0. $$
There are five coefficients (M, N, P, Q, and R) but your information is only four points. Assume M =1 and substitutes the values x and y for each point. You will get a linear system. Solve it and that's all.
answered Dec 3 '18 at 10:18
Antonio Luis
212
Or you can find the center and the semi-axes graphically (look at the picture).
– Antonio Luis
Dec 3 '18 at 10:20
Thanks for the solution Antonio, I am able to comprehend from your graphic solution. Turns out the four points are vertices of the ellipse, I am able to solve for the equation using the center and semi-axes.
– Matthew
Dec 3 '18 at 11:12
add a comment |
There are infinite ellipses determined by four points. By representing your four points the simplest option is a vertical ellipse.
In that case, first of all you must know the general equation of an ellipse
$$ Mx^2+Ny^2 +Px+Qy +R =0. $$
There are five coefficients (M, N, P, Q, and R) but your information is only four points. Assume M =1 and substitutes the values x and y for each point. You will get a linear system. Solve it and that's all.
answered Dec 3 '18 at 10:18
Antonio Luis
212
Or you can find the center and the semi-axes graphically (look at the picture).
– Antonio Luis
Dec 3 '18 at 10:20
Thanks for the solution Antonio, I am able to comprehend from your graphic solution. Turns out the four points are vertices of the ellipse, I am able to solve for the equation using the center and semi-axes.
– Matthew
Dec 3 '18 at 11:12
add a comment |
There are infinite ellipses determined by four points. By representing your four points the simplest option is a vertical ellipse.
In that case, first of all you must know the general equation of an ellipse
$$ Mx^2+Ny^2 +Px+Qy +R =0. $$
There are five coefficients (M, N, P, Q, and R) but your information is only four points. Assume M =1 and substitutes the values x and y for each point. You will get a linear system. Solve it and that's all.
answered Dec 3 '18 at 10:18
Antonio Luis
212
There are infinite ellipses determined by four points. By representing your four points the simplest option is a vertical ellipse.
In that case, first of all you must know the general equation of an ellipse
$$ Mx^2+Ny^2 +Px+Qy +R =0. $$
There are five coefficients (M, N, P, Q, and R) but your information is only four points. Assume M =1 and substitutes the values x and y for each point. You will get a linear system. Solve it and that's all.
answered Dec 3 '18 at 10:18
Antonio Luis
212
answered Dec 3 '18 at 10:18
Antonio Luis
212
answered Dec 3 '18 at 10:18
Antonio Luis
212
answered Dec 3 '18 at 10:18
Antonio Luis
212
212
Or you can find the center and the semi-axes graphically (look at the picture).
– Antonio Luis
Dec 3 '18 at 10:20
Thanks for the solution Antonio, I am able to comprehend from your graphic solution. Turns out the four points are vertices of the ellipse, I am able to solve for the equation using the center and semi-axes.
– Matthew
Dec 3 '18 at 11:12
add a comment |
Or you can find the center and the semi-axes graphically (look at the picture).
– Antonio Luis
Dec 3 '18 at 10:20
Thanks for the solution Antonio, I am able to comprehend from your graphic solution. Turns out the four points are vertices of the ellipse, I am able to solve for the equation using the center and semi-axes.
– Matthew
Dec 3 '18 at 11:12
Or you can find the center and the semi-axes graphically (look at the picture).
– Antonio Luis
Dec 3 '18 at 10:20
Or you can find the center and the semi-axes graphically (look at the picture).
– Antonio Luis
Dec 3 '18 at 10:20
Thanks for the solution Antonio, I am able to comprehend from your graphic solution. Turns out the four points are vertices of the ellipse, I am able to solve for the equation using the center and semi-axes.
– Matthew
Dec 3 '18 at 11:12
Thanks for the solution Antonio, I am able to comprehend from your graphic solution. Turns out the four points are vertices of the ellipse, I am able to solve for the equation using the center and semi-axes.
– Matthew
Dec 3 '18 at 11:12
add a comment |
If $A,B,C$,&$D$ are the 4 vertices of this ellipse then the intersection of $AC$ and $BD$ is the center of this ellipse which is $I(1,4)$
Now $IA=3$ and $IB=2$
Thus the equation of this ellipse is $$frac{(x-1)^2}{4}+frac{(y-4)^2}{9}=1$$
answered Dec 3 '18 at 10:39
Fareed AF
44211
Appreciate the solution kind sir
– Matthew
Dec 3 '18 at 11:12
@Matthew Your much welcome :)
– Fareed AF
Dec 3 '18 at 11:14
You’ve made a tacit assumption that the ellipse is axis-aligned. The question makes no mention of that.
– amd
Dec 3 '18 at 23:52
@amd True, but as they mentioned above, to define an ellipse we need 5 points, from 4 points you can't get the equation of an ellipse unless these 4 points are the vertices. Also I started my answer with if they are the vertices ...
– Fareed AF
Dec 4 '18 at 4:28
Fair enough. However, it is untrue that you can’t get the equation of an ellipse from four points—it’s just that there’s not a unique ellipse through those points. It’s a fairly simple matter to derive the equations of a one-parameter family of ellipses that all pass through those points.
– amd
Dec 4 '18 at 5:23
|
show 1 more comment
If $A,B,C$,&$D$ are the 4 vertices of this ellipse then the intersection of $AC$ and $BD$ is the center of this ellipse which is $I(1,4)$
Now $IA=3$ and $IB=2$
Thus the equation of this ellipse is $$frac{(x-1)^2}{4}+frac{(y-4)^2}{9}=1$$
answered Dec 3 '18 at 10:39
Fareed AF
44211
Appreciate the solution kind sir
– Matthew
Dec 3 '18 at 11:12
@Matthew Your much welcome :)
– Fareed AF
Dec 3 '18 at 11:14
You’ve made a tacit assumption that the ellipse is axis-aligned. The question makes no mention of that.
– amd
Dec 3 '18 at 23:52
@amd True, but as they mentioned above, to define an ellipse we need 5 points, from 4 points you can't get the equation of an ellipse unless these 4 points are the vertices. Also I started my answer with if they are the vertices ...
– Fareed AF
Dec 4 '18 at 4:28
Fair enough. However, it is untrue that you can’t get the equation of an ellipse from four points—it’s just that there’s not a unique ellipse through those points. It’s a fairly simple matter to derive the equations of a one-parameter family of ellipses that all pass through those points.
– amd
Dec 4 '18 at 5:23
|
show 1 more comment
If $A,B,C$,&$D$ are the 4 vertices of this ellipse then the intersection of $AC$ and $BD$ is the center of this ellipse which is $I(1,4)$
Now $IA=3$ and $IB=2$
Thus the equation of this ellipse is $$frac{(x-1)^2}{4}+frac{(y-4)^2}{9}=1$$
answered Dec 3 '18 at 10:39
Fareed AF
44211
If $A,B,C$,&$D$ are the 4 vertices of this ellipse then the intersection of $AC$ and $BD$ is the center of this ellipse which is $I(1,4)$
Now $IA=3$ and $IB=2$
Thus the equation of this ellipse is $$frac{(x-1)^2}{4}+frac{(y-4)^2}{9}=1$$
answered Dec 3 '18 at 10:39
Fareed AF
44211
edited Dec 3 '18 at 10:45
answered Dec 3 '18 at 10:39
Fareed AF
44211
answered Dec 3 '18 at 10:39
Fareed AF
44211
answered Dec 3 '18 at 10:39
Fareed AF
44211
44211
Appreciate the solution kind sir
– Matthew
Dec 3 '18 at 11:12
@Matthew Your much welcome :)
– Fareed AF
Dec 3 '18 at 11:14
You’ve made a tacit assumption that the ellipse is axis-aligned. The question makes no mention of that.
– amd
Dec 3 '18 at 23:52
@amd True, but as they mentioned above, to define an ellipse we need 5 points, from 4 points you can't get the equation of an ellipse unless these 4 points are the vertices. Also I started my answer with if they are the vertices ...
– Fareed AF
Dec 4 '18 at 4:28
Fair enough. However, it is untrue that you can’t get the equation of an ellipse from four points—it’s just that there’s not a unique ellipse through those points. It’s a fairly simple matter to derive the equations of a one-parameter family of ellipses that all pass through those points.
– amd
Dec 4 '18 at 5:23
|
show 1 more comment
Appreciate the solution kind sir
– Matthew
Dec 3 '18 at 11:12
@Matthew Your much welcome :)
– Fareed AF
Dec 3 '18 at 11:14
You’ve made a tacit assumption that the ellipse is axis-aligned. The question makes no mention of that.
– amd
Dec 3 '18 at 23:52
@amd True, but as they mentioned above, to define an ellipse we need 5 points, from 4 points you can't get the equation of an ellipse unless these 4 points are the vertices. Also I started my answer with if they are the vertices ...
– Fareed AF
Dec 4 '18 at 4:28
Fair enough. However, it is untrue that you can’t get the equation of an ellipse from four points—it’s just that there’s not a unique ellipse through those points. It’s a fairly simple matter to derive the equations of a one-parameter family of ellipses that all pass through those points.
– amd
Dec 4 '18 at 5:23
Appreciate the solution kind sir
– Matthew
Dec 3 '18 at 11:12
Appreciate the solution kind sir
– Matthew
Dec 3 '18 at 11:12
@Matthew Your much welcome :)
– Fareed AF
Dec 3 '18 at 11:14
@Matthew Your much welcome :)
– Fareed AF
Dec 3 '18 at 11:14
You’ve made a tacit assumption that the ellipse is axis-aligned. The question makes no mention of that.
– amd
Dec 3 '18 at 23:52
You’ve made a tacit assumption that the ellipse is axis-aligned. The question makes no mention of that.
– amd
Dec 3 '18 at 23:52
@amd True, but as they mentioned above, to define an ellipse we need 5 points, from 4 points you can't get the equation of an ellipse unless these 4 points are the vertices. Also I started my answer with if they are the vertices ...
– Fareed AF
Dec 4 '18 at 4:28
@amd True, but as they mentioned above, to define an ellipse we need 5 points, from 4 points you can't get the equation of an ellipse unless these 4 points are the vertices. Also I started my answer with if they are the vertices ...
– Fareed AF
Dec 4 '18 at 4:28
Fair enough. However, it is untrue that you can’t get the equation of an ellipse from four points—it’s just that there’s not a unique ellipse through those points. It’s a fairly simple matter to derive the equations of a one-parameter family of ellipses that all pass through those points.
– amd
Dec 4 '18 at 5:23
Fair enough. However, it is untrue that you can’t get the equation of an ellipse from four points—it’s just that there’s not a unique ellipse through those points. It’s a fairly simple matter to derive the equations of a one-parameter family of ellipses that all pass through those points.
– amd
Dec 4 '18 at 5:23
|
show 1 more comment
Four points are generally not enough to determine an ellipse uniquely. What other constraints do you have?
– amd
Dec 3 '18 at 9:43
@amd, there are no other constraints
– Matthew
Dec 3 '18 at 9:48
1
Plot the points, it certainly looks like you can say more about this ellipse.
– Paul
Dec 3 '18 at 9:53
Perhaps the principal axes of your ellipse are meant to be parallel to the coordinate axes? Otherwise, there is an infinite number of ellipses that pass through these points.
– amd
Dec 3 '18 at 9:54
@Paul I actually can't, this question is found on a highschool textbook
– Matthew
Dec 3 '18 at 9:57