Question

Show that the circles given by the following equations intersect each other orthogonally. x2 + y2 – 2x – 2y – 7 = 0, 3x2 +3y2 – 8x + 29y = 0.

Answer 1

C1 = (1, 1)

g = –1, f = –1, c = –7; g' = −4/3, f' = 29/6; c' = 0

Condition that two circles are orthogonal is 2gg' + 2ff' = c + c'

2(–1) (−4/3) + 2(–1) (29/6) = –7 + 0

L.H.*. = 8/3 - 29/3 = − 21/3 = –7

-7 = -7

Hence both circles cut orthogonally.