Area of region bounded by locus of a point P
$begingroup$
The area of the region bounded by the locus of point P satisfying d(P,A)=4, where A is (1,2) is _______ .
Where we define the distance between two points P(x,y) and Q(a,b) as $$d(P,Q)=max(|a-x|,|b-y|)$$.
My attempt
$$d(P,A)=max(|1-x|,|2-y|)$$
$$4=max(|1-x|,|2-y|)$$
Now it gives 4 cases to be equaled to 4 which gives different coordinates.
Then how will I know which coordinate to take?
analytic-geometry coordinate-systems locus
asked Oct 2 '18 at 0:52
jayant98jayant98
513116
$endgroup$
add a comment |
$begingroup$
The area of the region bounded by the locus of point P satisfying d(P,A)=4, where A is (1,2) is _______ .
Where we define the distance between two points P(x,y) and Q(a,b) as $$d(P,Q)=max(|a-x|,|b-y|)$$.
My attempt
$$d(P,A)=max(|1-x|,|2-y|)$$
$$4=max(|1-x|,|2-y|)$$
Now it gives 4 cases to be equaled to 4 which gives different coordinates.
Then how will I know which coordinate to take?
analytic-geometry coordinate-systems locus
asked Oct 2 '18 at 0:52
jayant98jayant98
513116
$endgroup$
add a comment |
$begingroup$
The area of the region bounded by the locus of point P satisfying d(P,A)=4, where A is (1,2) is _______ .
Where we define the distance between two points P(x,y) and Q(a,b) as $$d(P,Q)=max(|a-x|,|b-y|)$$.
My attempt
$$d(P,A)=max(|1-x|,|2-y|)$$
$$4=max(|1-x|,|2-y|)$$
Now it gives 4 cases to be equaled to 4 which gives different coordinates.
Then how will I know which coordinate to take?
analytic-geometry coordinate-systems locus
asked Oct 2 '18 at 0:52
jayant98jayant98
513116
$endgroup$
The area of the region bounded by the locus of point P satisfying d(P,A)=4, where A is (1,2) is _______ .
Where we define the distance between two points P(x,y) and Q(a,b) as $$d(P,Q)=max(|a-x|,|b-y|)$$.
My attempt
$$d(P,A)=max(|1-x|,|2-y|)$$
$$4=max(|1-x|,|2-y|)$$
Now it gives 4 cases to be equaled to 4 which gives different coordinates.
Then how will I know which coordinate to take?
analytic-geometry coordinate-systems locus
analytic-geometry coordinate-systems locus
asked Oct 2 '18 at 0:52
jayant98jayant98
513116
asked Oct 2 '18 at 0:52
jayant98jayant98
513116
edited Dec 7 '18 at 17:39
jayant98
asked Oct 2 '18 at 0:52
jayant98jayant98
513116
asked Oct 2 '18 at 0:52
jayant98jayant98
513116
asked Oct 2 '18 at 0:52
jayant98jayant98
513116
513116
add a comment |
add a comment |
1 Answer
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Maximum of two numbers is $4$ iff one of them is $4$ and the other one is $leq 4$. From this you can check that the locus consists of points on the rectangle with vertices $(-3,-2),(-3,6),(5,-2)$ and $(5,6)$. [For example, $|1-x|=4$ iff $x=-3$ or $x=5$]. The area of this rectangular region is 64.
answered Oct 2 '18 at 6:05
Kavi Rama MurthyKavi Rama Murthy
54.8k32056
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1 Answer
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1 Answer
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$begingroup$
Maximum of two numbers is $4$ iff one of them is $4$ and the other one is $leq 4$. From this you can check that the locus consists of points on the rectangle with vertices $(-3,-2),(-3,6),(5,-2)$ and $(5,6)$. [For example, $|1-x|=4$ iff $x=-3$ or $x=5$]. The area of this rectangular region is 64.
answered Oct 2 '18 at 6:05
Kavi Rama MurthyKavi Rama Murthy
54.8k32056
$endgroup$
add a comment |
$begingroup$
Maximum of two numbers is $4$ iff one of them is $4$ and the other one is $leq 4$. From this you can check that the locus consists of points on the rectangle with vertices $(-3,-2),(-3,6),(5,-2)$ and $(5,6)$. [For example, $|1-x|=4$ iff $x=-3$ or $x=5$]. The area of this rectangular region is 64.
answered Oct 2 '18 at 6:05
Kavi Rama MurthyKavi Rama Murthy
54.8k32056
$endgroup$
add a comment |
$begingroup$
Maximum of two numbers is $4$ iff one of them is $4$ and the other one is $leq 4$. From this you can check that the locus consists of points on the rectangle with vertices $(-3,-2),(-3,6),(5,-2)$ and $(5,6)$. [For example, $|1-x|=4$ iff $x=-3$ or $x=5$]. The area of this rectangular region is 64.
answered Oct 2 '18 at 6:05
Kavi Rama MurthyKavi Rama Murthy
54.8k32056
$endgroup$
Maximum of two numbers is $4$ iff one of them is $4$ and the other one is $leq 4$. From this you can check that the locus consists of points on the rectangle with vertices $(-3,-2),(-3,6),(5,-2)$ and $(5,6)$. [For example, $|1-x|=4$ iff $x=-3$ or $x=5$]. The area of this rectangular region is 64.
answered Oct 2 '18 at 6:05
Kavi Rama MurthyKavi Rama Murthy
54.8k32056
answered Oct 2 '18 at 6:05
Kavi Rama MurthyKavi Rama Murthy
54.8k32056
answered Oct 2 '18 at 6:05
Kavi Rama MurthyKavi Rama Murthy
54.8k32056
answered Oct 2 '18 at 6:05
Kavi Rama MurthyKavi Rama Murthy
54.8k32056
54.8k32056
add a comment |
add a comment |
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