Question

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

Solution

Correct option is

 

The sphere is .

 

 

 

   Centre = (–1, 1, 2) and radius = 5.

The plane is 

  CA = length of perpendicular from C(–1, 1, 2) to the plane

            

            = 4 < radius of sphere

 ∴ Given plane intersects the sphere.

 

 ∴ Radius of circle with centre at A = 3.

AC is normal to the given plane.

 ∴ D.r.’s of AC are 1, 2, 2. AC passes through C(–1, 1, 2).

 

Let the coordinates of A be (

Since, A lies on the plane, we have (

 

 

                                           

 

SIMILAR QUESTIONS

Q1

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

Q2

Find the value of  for which the plane  touches the sphere 

Q3

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

Q4

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

Q5

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.

Q6

Chord AB is a diameter of the sphere  with coordinates of A as (3, 2, –2). Find the coordinates of B.

Q7

A plane passes through a fixed point (­a, b, c) and cuts axes in A, B, C. Find the locus of the centre of the sphere OABC