Circle Ques 70
- 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
$(2002,1 M)$
4
(b) $2 \sqrt{5}$
5
(d) $3 \sqrt{5}$
Show Answer
Answer:
Correct Answer: 70.(c)
Solution:
Formula:
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
$$ \begin{alignedat} & =\sqrt{x _1^{2}+y _1^{2}+6 x _1+6 y _1-2} \\ & =\sqrt{0^{2}+3^{2}+6(0)+6(3)+2} \\ & =\sqrt{25}=5 \end{aligned} $$
BETA
