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)

A(-2,4, 2), B(5,2, -1)

You can still ask an expert for help

Wayne Everett

Answered 2022-07-26
Author has **19** answers

$r=|AB|=\sqrt{(5+2{)}^{2}+(2-4{)}^{2}+(-1-2{)}^{2}}=\sqrt{(7{)}^{2}+(2{)}^{2}+(3{)}^{2}}=\sqrt{62}$

$2|PA|=|PB|$

$2\sqrt{(x+2{)}^{2}+(x-4{)}^{2}+(z-2{)}^{2}}=\sqrt{(x-25{)}^{2}+(x-2{)}^{2}+(z+1{)}^{2}}$

$4((x+2{)}^{2}+(x-4{)}^{2}+(z-2{)}^{2})=(x-5{)}^{2}+(x-2{)}^{2}+(z+1{)}^{2}$

simplify obtain sphere

$2|PA|=|PB|$

$2\sqrt{(x+2{)}^{2}+(x-4{)}^{2}+(z-2{)}^{2}}=\sqrt{(x-25{)}^{2}+(x-2{)}^{2}+(z+1{)}^{2}}$

$4((x+2{)}^{2}+(x-4{)}^{2}+(z-2{)}^{2})=(x-5{)}^{2}+(x-2{)}^{2}+(z+1{)}^{2}$

simplify obtain sphere

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