Question

For the circle $x^2+y^2+6x+8y=0,$ and the points $P(-3,-6)$ and $Q(4,-2),$

• A. $P,Q$ lie inside the circle
• B. $P,Q$ lie outside the circle
• C. $P$ lies inside and $Q$ lies outside the circle
• D. $Q$ lies inside and $P$ lies outside the circle

Answer 1

The correct option is C $P$ lies inside and $Q$ lies outside the circle

Given circle $S:x^2+y^2+6x+8y=0$
Now putting $P(-3,-6)$ coordinates in the circle equation
$S_1:3^2+6^2-18-48=-21$
$\Rightarrow S_1<0$
So the point $P$ lies inside the circle.

Now putting $Q(4,-2)$ coordinates in the circle equation
$S_2:4^2+2^2+24-16=28>0$
$\Rightarrow S_2>0$
So the point $Q$ lies outside the circle.