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Q.

If A(3,0), B(-3,0) the locus of the point P such that $P A^{2} + P B^{2} = 18$ is $x^{2} + y^{2} = k$ then k = _____

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a

8

b

10

c

0

d

5

answer is A.

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Detailed Solution

$G i v e n : A (3, 0), B (- 3, 0) a n d P (x, y) b e s . t . P A^{2} + P B^{2} = 18, \Rightarrow {(x - 3)}^{2} + y^{2} + {(x + 3)}^{2} + y^{2} = 18 \Rightarrow x^{2} + 9 - 6 x + y^{2} + x^{2} + 9 + 6 x + y^{2} = 18 \Rightarrow x^{2} + y^{2} = 0 k = 0$

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