P is a point of intersection of the circles S x ^2+ y ^2-6 x +2 k y+1=0 and S^1 x^2+y^2+2 k x-6 y-7=0 . If the tangent at P to S=0 pass through the centre of S^1=0 and the tangent at P to S ^1=0 pass through the centre of S =0 , then the ra

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P is a point of intersection of the circles S x ^2+ y ^2-6 x +2 k y+1=0 and S^1 x^2+y^2+2 k x-6 y-7=0 . If the tangent at P to S=0 pass through the centre of S^1=0 and the tangent at P to S ^1=0 pass through the centre of S =0 , then the radius of S ^1=0 is

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Correct answer: D. 65 2

From given equation of circles aligned & C ^ (3,- k ), r ^ = 9+ k ^2-1 & and C ^ (- k , 3), r ^ = 9+ k ^2+7 aligned According to question aligned & CP ^2+ C ^ P ^2= CC ^ ( CPC ^ =90^ ) & 18+2 k ^2+6=2(3+ k )^2 k = 1 2 & Now, r ^ = 9+ k ^2+7 = 65 2 aligned

P is a point of intersection of the circles S x ^2+ y ^2-6 x +2 k y+1=0 and S^1 x^2+y^2+2 k x-6 y-7=0 . If the tangent at P to S=0 pass through the centre of S^1=0 and the tangent at P to S ^1=0 pass through the centre of S =0 , then the radius of S ^1=0 is

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