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Question

The perimeter of a triangle is 20 and the points (-2, -3) and (-2, 3) are two of the vertices of it. Then the locus of third vertex is :

A
(x2)249+y240=1
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B
(x+2)249+y240=1
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C
(x+2)240+y249=1
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D
(x2)240+y249=1
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Solution

The correct option is C (x+2)240+y249=1
A(2,3),B(2,3)
Let the third vertex be C(x,y)
AB + BC+CA=20
BC+CA=14
So locus of C is ellipse with A,B as focii.
2a=14
2ae=6
e=37
we get b as 40
Equation of ellipse is (x+2)240+y249=1

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