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Q.

P and Q are two variable points on the axes of $x$ and $y$ respectively such that $| O P | + | O Q | = a,$ then the locus of foot of perpendicular from origin on PQ is

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a

$(x - y) (x^{2} + y^{2}) = a x y$

b

$(x + y) (x^{2} + y^{2}) = a x y$

c

$(x + y) (x^{2} + y^{2}) = a (x - y)$

d

$(x + y) (x^{2} - y^{2}) = a x y$

answer is B.

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Detailed Solution

Question Image

Slope of OA is $\frac{y_{1}}{x_{1}}$
Sloper of $P Q = \frac{- x_{1}}{y_{1}}$
EQ.of PQ is $x x_{1} + y y_{1} = x_{1}^{2} + y_{1}^{2}$
OP+OQ=a
$\frac{x_{1}^{2} + y_{1}^{2}}{x_{1}} + \frac{x_{1}^{2} + y_{1}^{2}}{y_{1}} = a$
$\Rightarrow (x + y) (x^{2} + y^{2}) = a x y$

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