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Let O(0,0) and A(0, 1) be two fixed poin...

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

A

`9x^2+8y^2-8y=16`

B

`9x^2+8y^2+8y=16`

C

`8x^2+9y^2-9y=18`

D

`8x^2+9y^2+9y=18`

Text Solution

Verified by Experts

The correct Answer is:
A
Let the point p be (h,k)
`:.1+sqrt(h^2+k^2)+sqrt(h^2+(k-1)^(2))=4`
`impliessqrt(h^2+(k-1)^(2))=3-sqrt(h^2+k^2)`
`impliesh^2+k^2-2k+1=9=h^2+k^2-6sqrt(h^2+k^2)`
`implies3sqrt(h^2+k^2)=4+k`
`implies8k^2+9h^2-8k-16=0`
`implies9x^2+8y^2-8y=16` (required locus)
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