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Question

Let O(0,0) and A(0,1) be two fixed points. Then the locus of a point P such that the perimeter of AOP is 4, is:

A
9x28y2+8y=16
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B
9x2+8y28y=16
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C
8x29y2+9y=18
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D
8x2+9y29y=18
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Solution

The correct option is B 9x2+8y28y=16
Given,

OA+AP+OP=4
1+x2+(y1)2 + x2+y2=4
(x2+y2)2=(3x2+(y1)2)2
x2+y2=9+x2+y22y+16x2+(y1)2
3x2+(y1)2=(5y)
9(x2+(y1)2)=(5y)2
9x2+8y28y=16

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