Find an equation of the sphere containing all surface points P = (x, y, z) such that the distance from P to A(−3, 6, 3) is "twice the distance from P to" B(6, 2, −3).

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

lo.lll

step-by-step explanation: