Find the centre of the circle passing through (0,0) and (1,0) and touching the circle x²+y² = 9.

Question

Arun · Answer

Let the equation of circle is x² + y² + 2gx + 2fy + c = 0 centre = (-g,-f) radius = √(g²+f²-c) it passes through (0,0)&(1,0) so point satisfy the equation put (0,0) c = 0 put (1,0) g = -1/2 since the circle touches internally hence distance between centre = difference of radius centre of given circle = (0,0) radius = 3 √(g² + f²) = 3 - √(g²+f²-c) √(1/4 + f²) = 3 - √(1/4 + f²) √(1/4 + f²) = 3/2 1/4 + f² = 9/4 f² = 2 f = √2 or -√2 hence centre = (1/2,√2) or (1/2,-√2)

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Find the centre of the circle passing through (0,0) and (1,0) and touching the circle x²+y² = 9.

Find the centre of the circle passing through (0,0) and (1,0) and touching the circle x²+y² = 9.

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