Question

Find the equation of the sphere if one of its diameters has endpoints (9, 7, 5) and (10, 9, 8) which has been normalized so that the coefficient of x2 is 1.

Answer 1

Answer:

$(x-9.5)^2 +(y-8)^2 +(z-6.5)^2= \frac{14}{4} =3.5$

Step-by-step explanation:

Given that a sphere has one of its diameters has endpoints (9, 7, 5) and (10, 9, 8) which has been normalized so that the coefficient of x2 is 1.

We know centre of a sphere is the mid point of diameter.

Hence centre of sphere = $(\frac{9+10}{2}, \frac{7+9}{2}, \frac{5+8}{2} )\\=(9.5, 8, 6.5)$

Diameter length = distance between the given points

=$\sqrt{(9-10)^2+(7-9)^2+(5-8)^2} \\=\sqrt{14}$

Radius of sphere = half of diameter = $\frac{\sqrt{14} }{2}$

Using radius and centre we can write equation of sphere as

$(x-9.5)^2 +(y-8)^2 +(z-6.5)^2= \frac{14}{4} =3.5$