UPSEE Solved Model Paper 5

Let equation of the rectangular hyperbola be xy = c2 ... (i) and equation of circle be x2+y2 = r2 ... (ii)
Put y =

c2

x

in eq (ii) we get x2+

c4

x2

= r2
⇒ x4−r2x2+x4 = 0
⇒ Σx1 = 0
Σx1x2 = r2 (iii)
similarly Σy1 = 0 , Σy1y2 = Ω2 ... (iv)
Now, CP2+CQ2+CR2+CS2 =
= (x1=x2+x3+x4)2 - + (y1+y2+y3+y4)2 -
= 0 + 2r2+0+2r2 [from eqs (iii) and (iv)] = 4r2