CircleHard

Question

Let x2 + y2 - 2x - 2y = 0 & x2 + y2 + 2ax + 2ay + b = 0 are two different circles. If L is the only common tangent of these circles such that their centers are mirror images in L, then which can be true -

Options

A.a + b = 13
B.a - b = 10
C.line L is x + y = 4
D.line L is x + 2y = 5

Solution

         
Possible when two circles touch each other & having same radii
r1 = r2 ⇒ √2 =
c1c2 = r1 + r2
⇒
⇒ a = - 3 & b = 16
Line L is x + y = 4

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