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

a line is an defined derm because it

a)contains an infinite number of points b) can be used to create other geometric shapes c)describes something that does not have width or depth d) is a term that does not have a formal definition. a line is an undefined term because it: contains an infinite number of points.

2 apples

step-by-step explanation:

taking away equals subtraction. 6-4=2