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A circle passes through (0,0),(6,0) and is tangent to the circle $x^{2} + y^{2} = 64$ then its y-intercept has magnitude

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$2 \sqrt{7}$

$2 \sqrt{3}$

$3 \sqrt{2}$

answer is D.

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Detailed Solution

Centre $= (3, \sqrt{7})$
Question Image
Equation ${(x - 3)}^{2} + {(y - \sqrt{7})}^{2} = 16 \Rightarrow x^{2} = y^{2} - 6 x - 2 \sqrt{7} y = 0$
Put $x = 0 \Rightarrow y = 2 \sqrt{7}$
Lengths of y intercept $= 2 \sqrt{7}$

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