# Find the equations of the circles of radius 5 whose centers lie on the x-axis and pass through the point (2,3).

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by nivedhitha

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by nivedhitha

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As radius =5, distance between (a,0) and (2,3) is 5.

==> (a - 2)² + (0 - 3)² = 5²

or a² - 4a - 12 = 0 or (a - 6)(a + 2) = 0

Hence points on x-axis are (6,0) an (-2,0) which are the centres of desired circles.

Hnce equations of circle are :-

(x - 6)² + (y - 0)² = 5² and (x + 2)² + (y - 0 )² = 5²

These are:- x² - 12x + y² +11 = 0 and x² + 4x + y² - 21 = 0