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Given that the circles \mathrm{x^2+y^2-4 x-5=0} and \mathrm{x^2+y^2+6 x-2 y+6=0} Let P be a point (α, β), then find the relation between α and β such that the tangents from P to both the circles are of equal length. Then find the relation between α and β.

 

Option: 1

\mathrm{9\alpha -\beta +10=0}


Option: 2

\mathrm{10\alpha -2\beta +11=0}


Option: 3

\mathrm{10\alpha -\beta +12=0}


Option: 4

\mathrm{\alpha -9\beta +11=0}


Answers (1)

best_answer

Lengths of tangents from P (α, β) to the circles are equal

\mathrm{\begin{aligned} & \Rightarrow \sqrt{\alpha^2+\beta^2-4 \alpha-5}=\sqrt{\alpha^2+\beta^2+6 \alpha-2 \beta+6} \\ & \Rightarrow 10 \alpha-2 \beta+11=0 . \end{aligned}}

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Ritika Jonwal

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