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Number of Common Tangents to Two Circles in Different Conditions

If the length...

Question

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

- 6

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- 4

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4

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13 / 2

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Solution

The correct option is A $- 4$
Length of Tangent from (5,3) $= \sqrt{5^{2} + 3^{2} + 2 * 5 + k * 3 + 17} = 7 \Rightarrow 3 k + 25 + 9 + 10 + 17 = 49 \Rightarrow 3 k = 49 - 61 \Rightarrow 3 k = - 12 \Rightarrow k = - 4$

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