If a circle passes through the point 1,1 and cuts the circle x 2 + y 2 = 1 orthogonally, then the locus of its centre is

Question

If a circle passes through the point 1,1 and cuts the circle x 2 + y 2 = 1 orthogonally, then the locus of its centre is, x 2 + y 2 - 3 x - 3 y + 1 = 0, 2 x + 2 y - 1 = 0, x 2 + y 2 - 2 x - 2 y + 1 = 0, 2 x + 2 y - 3 = 0

MARKS App · Accepted Answer

Let the centre of the circle be α , β . Since it cuts the circle x 2 + y 2 = 1 orthogonally, 2 - α × 0 + 2 - β × 0 = c 1 - 1 ⇒ c 1 = 1 ∴ The equation of the circle is x 2 + y 2 - 2 α x - 2 β y + 1 = 0 It passes through 1 , 1 . So 1 + 1 - 2 α - 2 β + 1 = 0 Hence, the locus of α , β is 2 x + 2 y - 3 = 0

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