Find the equation of the sphere with points P such that the distance from P to A is twice the distance from P to B. A(-2,4, 2), B(5,2, -1)

Baladdaa9 2022-07-25 Answered
Find the equation of the sphere with points P such that the distance from P to A is twice the distance from P to B.
A(-2,4, 2), B(5,2, -1)
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Answers (1)

Wayne Everett
Answered 2022-07-26 Author has 19 answers
r = | A B | = ( 5 + 2 ) 2 + ( 2 4 ) 2 + ( 1 2 ) 2 = ( 7 ) 2 + ( 2 ) 2 + ( 3 ) 2 = 62
2 | P A | = | P B |
2 ( x + 2 ) 2 + ( x 4 ) 2 + ( z 2 ) 2 = ( x 25 ) 2 + ( x 2 ) 2 + ( z + 1 ) 2
4 ( ( x + 2 ) 2 + ( x 4 ) 2 + ( z 2 ) 2 ) = ( x 5 ) 2 + ( x 2 ) 2 + ( z + 1 ) 2
simplify obtain sphere
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