If ratio of lengths of tangents drawn from point (f,g) to given circle {x^2} + {y^2} = 6 and {x^2} +

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10-1.Circle and System of Circles

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If the ratio of the lengths of tangents drawn from the point $(f,g)$ to the given circle ${x^2} + {y^2} = 6$ and ${x^2} + {y^2} + 3x + 3y = 0$ be $2 : 1$, then

A

${f^2} + {g^2} + 2g + 2f + 2 = 0$

B

${f^2} + {g^2} + 4g + 4f + 4 = 0$

C

${f^2} + {g^2} + 4g + 4f + 2 = 0$

D

None of these

Solution

(c) According to the condition,

$\frac{{{f^2} + {g^2} – 6}}{{{f^2} + {g^2} + 3f + 3g}} = \frac{4}{1}$

$ \Rightarrow {f^2} + {g^2} + 4f + 4g + 2 = 0$.

Standard 11

Mathematics

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