How do you find an equation of the sphere with center (1, −7, 4) and radius 5?

1 Answer
smendyka
Dec 18, 2017

See a solution process below:

Explanation:

The general equation for a sphere of radius color(red)(R)R with center at (color(blue)(a), color(green)(b), color(purple)(c))(a,b,c) is:

(x-color(blue)(a))^2 + (y-color(green)(b))^2 + (z-color(purple)(c))^2 = color(red)(R)^2(x−a)2+(y−b)2+(z−c)2=R2

Substituting the information from the problem gives:

(x-color(blue)(1))^2 + (y-color(green)(-7))^2 + (z-color(purple)(4))^2 = color(red)(5)^2(x−1)2+(y−−7)2+(z−4)2=52

(x-color(blue)(1))^2 + (y+color(green)(7))^2 + (z-color(purple)(4))^2 = color(red)(25)(x−1)2+(y+7)2+(z−4)2=25

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