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

Question

Dr. Abubacker · Accepted Answer

(c)
$x^{2} + y^{2} + 6x + 6y - 2 = 0$
Centre $( - 3,\  - 3)$, radius $= \sqrt{9 + 9 + 2} = \sqrt{20}$
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Now, $\mathcal{Q}C = \sqrt{( - 3)^{2} + 6^{2}} = \sqrt{45}$
In right $\mathrm{\Delta}CP\mathcal{Q}$
$P\mathcal{Q} = \sqrt{45 - 20} = 5$

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

Explanation

Reviewed by Dr. Abubacker

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