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IIT-JEE 1978

Subjective
Find the equation of the circle whose radius is 5 and which touches the circle $${x^2}\, + \,{y^2}\, - \,2x\,\, - 4y\, - 20 = 0\,$$ at the point (5, 5).

$${x^2}\, + \,{y^2}\, - \,18x\,\, - 16y\, + 120 = 0\,$$

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