Question

Q.4 Find the centre and radius of the circle in which sphere x + y + z² + 2x - 2y - 4z - 19
= 0 is cut by the plane x + 2y + 2z + 7 = 0.​

Answer 1

Answer:

Centre and radius of the given sphere are (−1,1,2) and

1

2

+1

2

+2

2

+19

=5 respectively

Now the perpendicular distance between centre of sphere to the given plane is given by,

d=

∣

∣

∣

∣

∣

1

2

+2

2

+2

2

−1+2(1)+2(2)+7

∣

∣

∣

∣

∣

=4

Therefore radius of the circle in which the given sphere and plane cut is

=

5

2

−4

2

=3