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The locus of P(x,y) such that sqrt(x^2+...

The locus of `P(x,y)` such that `sqrt(x^2+y^2+8y+16)-sqrt(x^2+y^2-6x+9)=5,` is

A

A. hyperbola

B

B. circle

C

C. finite line segment

D

D. infinite ray

Text Solution

Verified by Experts

The correct Answer is:
D
We have `sqrt(x^(2)+(y+4)^(2)) -sqrt((x-3)^(2)-y^(2))=5`. The distance between the two points (3,0) and `(0,-4)` is 5.

Locus of P is the part of line `(x)/(3) -(y)/(4) =1`.
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