If the length of the tangent drawn from any point on the circle $x^{2} + y^{2} + 15 x - 17 y + c^{2} = 0$ to the circle $x^{2} + y^{2} + 15 x - 17 y + 21 = 0 i s \sqrt{5}$ units , then $c$ is equal to

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Solution

The correct options are
C $4$
D $- 4$
Required length
$\sqrt{x^{2} + y^{2} + 15 x - 17 y + 21 - (x^{2} + y^{2} + 15 x - 17 y + c^{2})} = \sqrt{5}$
$\Rightarrow \sqrt{21 - c^{2}} = \sqrt{5} \Rightarrow c^{2} = 16 \Rightarrow c = \pm 4$

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