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Answer:
Equation of Sphere = +
+
- 18x - 4/3y +10z + 142/3 = 0
Step-by-step explanation:
Data Given:
P = (x,y,z)
Distance from P to A (-3,6,3) = Twice the distance from P to B(6,2,-3)
Solution:
Find the equation of the sphere:
It is given that:
PA = 2PB
Squaring both sides:
+
+
= 4 x
+
+
Solving the above equation:
+
+
= 4 x {
+
+
}
+ 9 + 6x +
+ 36 - 12y +
+ 9 - 6z = 4 {
+ 36 - 12x +
+ 4 - 4y +
+ 9 + 6z}
+ 9 + 6x +
+ 36 - 12y +
+ 9 - 6z = 4
+ 144 - 48x +4
+ 16 - 16y + 4
+ 36 + 24z
Putting the right hand side = 0 and solving the equation:
- 4
+
- 4
+
- 4
+ 6x + 48x - 12y +16y -6z - 24z + 9 + 36 + 9 -144 - 16 - 36 = 0
-3 - 3
-3
+ 54x + 4y -30z -142 = 0
Taking (-) common
- ( 3 + 3
+ 3
- 54x - 4y +30z + 142) = 0
3 + 3
+ 3
- 54x - 4y +30z + 142 = 0
dividing the whole equation by 3
+
+
- 54/3x - 4/3y +30/3z + 142/3 = 0
+
+
- 54/3x - 4/3y +30/3z + 142/3 = 0
+
+
- 18x - 4/3y +10z + 142/3 = 0