Question

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

Solution

Correct option is

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

Q1

 

Find the centre and radius of the sphere

             

Q2

 

Find the equation of the sphere concentric with the sphere

  and double its radius.

Q3

A point P(x, y, z) is such that 3PA = 2PB, where 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.

Q4

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

Q5

Find the value of  for which the plane  touches the sphere 

Q6

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

Q7

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

Q8

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.