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Point Form of Tangent: Ellipse

Tangent drawn...

Question

Tangent drawn to circle $(x - 1)^{2} + (y - 1)^{2} = 5$ at point P meets the line $2 x + y + 6 = 0$ at Q on the X-axis. Length PQ is equal to

\sqrt{12}

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\sqrt{10}

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4

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\sqrt{15}

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Solution

The correct option is C $\sqrt{12}$
Point on x axis $= (- 3, 0)$
Center of circle $= (1, 1)$
Length of tangent, from the figure
$= \sqrt{17 - 5}$
$= \sqrt{12}$

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