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

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10-1.Circle and System of Circles

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

A

$4$

B

$-4$

C

$-6$

D

$13\over2$

Solution

(b) According to the condition,

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

$ \Rightarrow $$61 + 3k = 49 \Rightarrow k = – 4$.

Standard 11

Mathematics

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