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Work Done When Force Is Varying

lf Aa, O, ...

Question

lf $A$ (a, $O$ ), $B (- a, O)$ then the locus of the point $P$ such that $(P A)^{2} + (P B)^{2} = 2. c^{2}$ is:

x^{2} + y^{2} + a^{2} - c^{2} = 0

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x^{2} + y^{2} + a^{2} + c^{2} = 0

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2 x^{2} + y^{2} + 3 a^{2} - c^{2} = 0

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x^{2} + y^{2} + a^{2} + 2 c^{2} = 0

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Solution

The correct option is A $x^{2} + y^{2} + a^{2} - c^{2} = 0$
Consider an arbitrary point $P (h, k)$ then using distance formula and the given relation in the question,
$(P A)^{2} + (P B)^{2} = 2. c^{2}$
$(h - a)^{2} + (k - 0)^{2} + (k + a)^{2} + (k - 0)^{2} = 2 C^{2}$
$h^{2} + k^{2} + a^{2} = c^{2}$
$x^{2} + y^{2} + a^{2} - c^{2} = 0$

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