CircleEasy
Question
If a circle passes through the point (a, b) and cuts the circle x2 + y2 = 4 orthogonally, then the locus of its centre is
Options
A.2ax + 2by + (a2 + b2 + 4) = 0
B.2ax + 2by - (a2 + b2 + 4) = 0
C.2ax - 2by + (a2 + b2 + 4) = 0
D.2ax - 2by - (a2 + b2 + 4) = 0
Solution
Let the circle be x2 + y2 + 2gx + 2fy + c = 0 ⇒ c = 4 and it passes through (a, b)
⇒ a2 + b2 + 2ga + 2fb + 4 = 0.
Hence locus of the centre is 2ax + 2by - (a2 + b2 + 4) = 0.
⇒ a2 + b2 + 2ga + 2fb + 4 = 0.
Hence locus of the centre is 2ax + 2by - (a2 + b2 + 4) = 0.
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