Question

The radius of the circle in which the sphere $x^2+y^2+z^2+2x-2y-4z-19=0$ is cut by the plane $x+2y+2z+7=0$ is

• A. 2
• B. 3
• C. 4
• D. 1

Answer 1

The correct option is B 3

Centre of the sphere is (-1, 1, 2) and its radius is $\sqrt{1+1+4+19}=5$
Length of the perpendicular from the centre on the plane is $\left|\frac{-1+2+4+7}{\sqrt{1+4+4}}\right|=4$
Radius of the sphere will be the hypotenuse of the traingle formed by the radius of the circle, perpendicular distance and radius of spehere.
So we get, radius of the required circle equal to $\sqrt{5^2-4^2}=3$.