Question

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.

Solution

Correct option is

 

We have         .

By the given condition, 3PA = 2PB.

 

 

 

 

 This represents a sphere.

SIMILAR QUESTIONS

Q1

Find the equation of the sphere whose centre is (2, – 3, 4) and radius 5.

Q2

 

Find the centre and radius of the sphere

 

Q3

 

Find the centre and radius of the sphere

 

Q4

 

Find the centre and radius of the sphere

             

Q5

 

Find the equation of the sphere concentric with the sphere

  and double its radius.

Q6

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

Q7

Find the value of  for which the plane  touches the sphere 

Q8

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