Question

Use the given information to answer the following questions. center (3, -9, 3), radius 5 (a) Find an equation of the sphere with the given center and radius. (b) What is the intersection of this sphere with the yz-plane?

Answer 1

Answer: The equation of the sphere with the center and radius

$x^{2} +y^{2} +z^{2}-6 x+18 y-6 z+74=0$

b) The intersection of this sphere with the y z-plane the x- co-ordinate

is zero(i.e., x = 0 )

Step-by-step explanation:

a) The equation of the sphere having center (h,k,l) and radius r is

$(x-h)^{2} +(y-k)^2+(z-l)^2 = r^2$

Given center of the sphere  (3, -9, 3) and radius 5

$(x-3)^{2}+(y+9)^2+(z-3)^2 = 5^2$

on simplification , we get solution

$x^{2} -6 x+9+y^{2} +18 y+81+z^{2}-6 z+9=25$

$x^{2} +y^{2} +z^{2}-6 x+18 y-6 z+74=0$

Final answer :-

$x^{2} +y^{2} +z^{2}-6 x+18 y-6 z+74=0$

b) The intersection of this sphere with the y z-plane the x- co-ordinate

is zero(i.e., x = 0 )

$y^{2} +z^{2}+18 y-6 z+74=0$