Find an equation of the sphere that passes through the origin and whose center is (1, 10, -5).

Question

Find an equation of the sphere that passes through the origin and whose center is (1, 10, -5).

Answer 1

Use the distance equation to find the radius.

 

Origin is (0,0,0) therefore,

 

d² = (x_f-x_i)² + (y_f-y_i)² +(z_f-z_i)²

 

d² = (1-0)²+(10-0)²+(-5-0)²

 

d²=1+100+25=126

 

Now use the equation for a sphere

 

(x-x_c)²+(y-y_c)²+(z-z_c)²=r²

 

(x-1)²+(y-10)²+(z+5)²=126