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  • If the tangent at a point on the circle <img alt="\mathrm{x^{2}+y^{2}+6 x+6 y=2}" src="https://entranc

If the tangent at a point \mathrm{P}on the circle \mathrm{x^{2}+y^{2}+6 x+6 y=2} meets the straight line \mathrm{5 x-2 y+6=0} at a point \mathrm{Q} on y-axis, then the length \mathrm{PQ} is:

Option: 1

4


Option: 2

2 \sqrt{5}


Option: 3

5


Option: 4

3 \sqrt{5}


Answers (1)

best_answer

\mathrm{x^{2}+y^{2}+6 x+6 y-2=0}

The line \mathrm{5 x-2 y+6=0} meets the y-axis at \mathrm{Q(0,3)}

Length of tangent drawn from \mathrm{Q} , i.e.

\mathrm{P Q=\sqrt{S_{1}}=\sqrt{0+9+0+18-2}=5 \: units}

Hence (C) is the correct answer.

Posted by

avinash.dongre

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