find the equation of plane to the sphere x^2 + y^2 + z^2 = 100 at point (3,-5,6)...
Answers
Answered by
0
Answer:
Let the equation of sphere.
x
2
+y
2
+z
2
+2ux+2vy+2wz+d=0
Because the points (0,0,2) lies on the sphere, hence.
0
2
+0
2
+2
2
+2u⋅0+2v⋅0+2w⋅z+d=0
⇒4w+d=−4
Point (0,2,0) lies on sphere hence
0
2
+2
2
+0
2
+2u⋅0+2v⋅2+2w⋅0+d=0
⇒4v+d=−4 .
Point (2,0,0) lies on the sphere hence
2
2
+0
2
+0
2
+2u⋅2+2v⋅2+2w⋅0+d=0
⇒4u+d=−4
∵ Centre of sphere (−u,−v,−w) lies on the plane x+y+z=2
∴−u−v−w=2
Solving equation (2), (3), (4) and (5)
u=−
3
2
,v=−
3
2
,w=
3
2
and d=−
3
4
Putting the value of u,v,w and d in equation (1) then required equation of sphere is
x
2
+y
2
+z
2
2(−
3
2
)x+2(−
3
2
)x+2(−
3
2
)y+2(−
3
2
)z
3
4
x
2
+y
2
+z
2
−
3
4
x−
3
4
y−
3
4
z−
3
4
3x
2
+3y
2
+3z
2
−4x−4y−4z−4=0.
Similar questions