find equation of a sphere having the circle x2+y2+z2+10y-4z-8=0,x+y+z=3 as the great circle.
Answers
Answered by
2
Answer:
Any sphere through the intersection of the given circle
x
2
+y
2
+z
2
+10y−4z−8=0 ...(1)
x+y+z=3 ...(2)
is x
2
+y
2
+z
2
+10y−4z−8+k(x+y+z−3)=0
⇒x
2
+y
2
+z
2
+kx+(10+k)y−(4−k)z−8−3k=0 ...(3)
Now if the circle of intersection of (1) and (2) is a greater circle of sphere (3), then
C(−
2
k
,−
2
(10+k)
,−
2
4−k
) of sphere (3) must lie on the plane (2) i.e., we must have
−
2
k
−(
2
10+k
)+
2
4−k
−3=0
⇒−k−10−k+4−k−6=0⇒−3k−12=0
⇒k=−4
Substitute k=−4 in (3), the required sphere is x
2
+y
2
+z
2
−4x+6y−8z+4=0.
Similar questions