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Properties of Radical Axis

If the length...

Question

If the length of tangent drawn from the point (5,3) to the circle $x^{2} + y^{2} + 2 x + k y + 17 = 0$ be 7, then k =

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-4

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-6

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13/2

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Solution

The correct option is B
-4

According to the condition,

$\sqrt{(5)^{2} + (3)^{2} + 2 (5) + k (3) + 17} = 7$

$\Rightarrow 61 + 3 k = 49 \Rightarrow k = - 4$

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