Circle 3 Question 8
8. If the tangent at the point $P$ on the circle $x^{2}+y^{2}+6 x+6 y=2$ meets the straight line $5 x-2 y+6=0$ at a point $Q$ on the $Y$-axis, then the length of $P Q$ is
$(2002,1 M)$
(a) 4
(b) $2 \sqrt{5}$
(c) 5
(d) $3 \sqrt{5}$
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Answer:
Correct Answer: 8. (c)
Solution:
- The line $5 x-2 y+6=0$ meets the $Y$-axis at the point $(0,3)$ and therefore the tangent has to pass through the point $(0,3)$ and required length
$$ \begin{aligned} & =\sqrt{x _1^{2}+y _1^{2}+6 x _1+6 y _1-2} \\ & =\sqrt{0^{2}+3^{2}+6(0)+6(3)-2} \\ & =\sqrt{25}=5 \end{aligned} $$
