Question

Which is the equation for a sphere with the center (2,-9,-1) and radius √r? a. (x + 2)2 + (y - 9)2 + ( z - 1)2 = r b. (x - 2)2 + (y + 9)2 + ( z + 1)2 = r c. (x - 2)2 + (y + 9)2 + ( z + 1)2 = √r d. (x + 2)2 + (y - 9)2 + ( z - 1)2 = r2

Answer 1

Answer: b.
`(x-2)^2+(y+9)^2+(z+1)^2=r`

Explanation:

The general equation of a sphere is :
`(x - a)^2 + (y - b)^2+ (z - c)^2 = R^2`, where (a, b, c) represents the center of the sphere, R represents the radius, and x, y, and z are the coordinates of the points on the surface of the sphere.

Given, Center of the sphere = (2,-9,-1)

Radius = √r

Then, the equation of the sphere would be

`(x - 2)^2 + (y - (-9))^2+ (z - (-1))^2 = (√(r))^2\\\\\Rightarrow\ (x-2)^2+(y+9)^2+(z+1)^2=r`

Hence, the correct option is b.
`(x-2)^2+(y+9)^2+(z+1)^2=r` .