BITSAT 2011 Paper

Let the two circles be x2+y2+2g1x+2f1y+c1 = 0 and x2+y2+2g2x+2f2y+c2 = 0
where g1 = 5/2, f1 = 3/2, c1 =7, g2 =–4, f2 =3 and c2 = k
If the two circles intersects orthogonally, then
2 (g1g2+f1f2) = c−1+c2 ⇒ 2 (−10+

9

2

) = 7 + k
⇒ 11 = 7 + k ⇒ k = 18