Question

Find the equation of the sphere passing through P(negative 4 comma 7 comma 6 )and Q(8 comma negative 3 comma 5 )with its center at the midpoint of PQ. ?

Answer 1

Answer: The equation of the sphere is:

(x-2)^2 + (y-2)^2 + (z-5/2)^2 = sqrt(245)/2

Explanation:

The centre of the sphere is the midpoint of the diameter, which is

1/2

[(-4,7,6) + (8,-3,5)] =(2,2,5/2)

The length of the diameter is

=sqrt |(8,-3,5) - (-4,7,6)|^2

=sqrt (12^2 + (-10)^2 + (-1)^2)

=sqrt (144+100+1)

=sqrt(245)

so the radius of

the sphere is:

1/2(sqrt(245)) = sqrt(245)/2.

The equation of the sphere is:

(x-2)^2 + (y-2)^2 + (z-5/2)^2 = sqrt(245)/2