Question

Let C be a curve which is locus of the point of the intersection of lines x = 2 + m and my = 4 – m. A circle (x – 2)² + (y + 1)² = 25 intersects the curve C at four points P, Q, R and S. If O is the centre of curve ‘C’ than OP² + OQ² + OR² + OS² is

(a)  25

(b)  50

(c)   25/2

(d)  100

Answer 1

Correct option  (d)  100

Explanation:

x – 2 = m

y + 1 = 4/m

(x–2)(y+1) = 4

XY = 4, where X = x – 2 and Y = y + 1

and (x – 2)2 + (y + 1)2 = 25

X² + Y² = 25

 Curve C and circle both are concentric.

∴ OP² + OQ² + OR² + OS² = 4r²

= 4 (25) = 100