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Circle

Lines are dra...

Question

Lines are drawn through the point P(-2, -3) to meet the circle $x^{2} + y^{2} - 2 x - 10 y + 1 = 0$ . The length of the line segment PA.A being the point on the circle where the line meets the circle at coincident points, is

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4 \sqrt{3}

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None of these

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Solution

The correct option is B $4 \sqrt{3}$
Equation of circle is $x^{2} + y^{2} - 2 x - 10 y + 1 = 0$
Point it is passing through $(- 2, - 3)$
length of tangent is $\sqrt{(- 2)^{2} + (- 3)^{2} - 2 (- 2) - 10 (- 3) 1)} \sqrt{4 + 9 + 4 + 30 + 1} \sqrt{48} = 4 \sqrt{3}$

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