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Let C be a curve which is the locus of the point of intersection of lines x = 2 + m and my = 4 – m. A circle of radius 5 concentric with C intersect the curve C at P,Q,R,S. If O is centre of the curve C, then $O P^{2} + O Q^{2} + O R^{2} + O S^{2}$ = ____

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25/2

answer is B.

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Detailed Solution

Curve x – 2 = m
$O P^{2} + y + 1 = \frac{4}{m}$
$4 \times 2$
$∴ (x - 2) (y + 1) = 4$
or XY = 4
Where X = x – 2
Y = y + 1
$S \equiv {(x - 2)}^{2} + {(y + 1)}^{2} = 25$
or $x^{2} + y^{2} = 25$

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