Q 38 - Calculus

Question

Find the center and radius of the sphere with the given equation:

$x^2+y^2+z^2-2x+6y-8z+17=0$

Step-by-Step Solution

Answer

The center is (1, -3, 4) and radius is 3.

Given information

The given equation of a sphere is: $x^2+y^2+z^2-2x+6y-8z+17=0$

Finding the radius and center

Converting the equation to whole square in variables$x,y \mathrm{and} z:$

$x^2+y^2+z^2-2x+1+6y+9-8z+16+17-26=0$

Isolating the variables:

${(x-1)}^2+{(y+3)}^2+{(z-4)}^2=3^2$

Comparing with equation of sphere, center is at (1, -3, 4) and radius is 3.