Question

The radius of circle made by meeting the plane $x+2y+2z+7=0$ to the sphere $x^2+y^2+z^2+2x-2y-4z-19=0$ is

• A. $5$
• B. $4$
• C. $3$
• D. None of these

Answer 1

Answer: (C)

$3$

Given plane is $x+2y+2z+7=0$ ........ $\left(i\right)$

Sphere is $x^2+y^2+z^2+2x-2y-4z-19=0$ ........ $\left(ii\right)$

The centre of sphere $C=(-1,1,2)$ and radius of sphere $r=\sqrt{1+1+4+9}=5$
Now, perpendicular distance of centre from plane is
$p=\frac{-1+2+4+7}{\sqrt{1+4+4}}=4$
$\therefore$ Radius of circle $r^{\prime }=\sqrt{r^2-p^2}=\sqrt{25-16}$
$=3$.