Use the following information to find the distance between Point A and Point B.

Question

Use the following information to find the distance between Point A and Point B.

Point A is the center of the sphere x² + 4x + y² + z² − 2z = 0.

Point B lies in the middle of the line segment connecting the points P₀(1, 3, 1) and P₁(−3, 5, 1).

Answer 1

The first step is to complete the square of the sphere equation by adding 4 to both sides.

x² + 4 x + 4 + y² + z² = 4

(x + 2) ² + y² + z² = 2²

This is the equation of a sphere with center at ( -2, 0 ,0) and radius 2

The midpoint of the line segment is (-1, 4 , 1)

The distance formula can be used to get the distance between (-2,0,0) and (-1, 4, 1)

The result is sqrt(18)