## Question

Find the radius of the circular section of the sphere by the plane

### Solution

4

The equation of the sphere is

∴ Centre and radius of the sphere are (0, 0, 0) and 5 respectively.

The equation of the plane is

OA = length of perpendicular from the origin to the plane

∴ Given plane intersects the sphere.

∴ Radius of the circular section of the sphere is **4.**

#### SIMILAR QUESTIONS

Find the centre and radius of the sphere

Find the equation of the sphere concentric with the sphere

and double its radius.

A point *P*(*x, y, z*) is such that 3*PA = *2*PB*, where *A *and *B* are the points (1, 3, 4) and (1, – 2, –1) respectively. Find the equation of the locus of the point *P* and show that the locus is a sphere.

Find the equation of the sphere whose centre has the position vector and which touches the plane

Find the value of for which the plane touches the sphere

Find the centre and radius of the circle in which the plane intersects the sphere

Find the equation of the sphere passing through the points (0, 0, 0), (–1, 2, 0), (0, 1, –1) and (1, 2, 5).

Find the equation of the sphere which passes through the points (1,–3, 4), (1, –5, 2), (1, –3, 0) and has its centre on the plane *x + y + z = *0.