I just got done taking a math test and we had the followingquestion: \"Find the

Question

I just got done taking a math test and we had the followingquestion:
"Find the equation for a sphere with a center at point P andpassing through point Q. P = <1,2,3> Q = <3,-3,4>"
My answer was reached using the following steps: 1. I figured a generic sphere at the origin wasx2 + y2 + z2 =1 2. To move the sphere to the new origin I did this:(x2-1)+ (y2-2)+ (z2-3)= 1 3. I then plugged in Q for x, y, and z and solved that to giveme the equation: (x2-1)+ (y2-2)+ (z2-3)=28
Is that even remotely correct?
Thanks for the help!
"Find the equation for a sphere with a center at point P andpassing through point Q. P = <1,2,3> Q = <3,-3,4>"
My answer was reached using the following steps: 1. I figured a generic sphere at the origin wasx2 + y2 + z2 =1 2. To move the sphere to the new origin I did this:(x2-1)+ (y2-2)+ (z2-3)= 1 3. I then plugged in Q for x, y, and z and solved that to giveme the equation: (x2-1)+ (y2-2)+ (z2-3)=28
Is that even remotely correct?
Thanks for the help!

Explanation / Answer

Almost. The general equation of a sphere is of the form (x-c1)2 + (y - c2)2 + (z-c3)2 = r2 , where C(c1,c2 ,c3) is the centre and r is theradius. The radius could be found using the distance formula to findthe distance from the centre to the point. D = ((3-1)2 + (-3 - 2)2 +(4-3)2) D = 30 Thus the radius is 30 and r2 is 30 The equation is (x -1)2+ (y-2)2+(z-3)2 = 30

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