Finding equation of curve form a point using equal distance

Hi guys, need help with this problem please,

A point P(x, y) moves in the x-y plane such that the distance from the line x=3 is always equal to the distance form the point (-6, 2).

Prove that the locus of P can be represented by a curve C with equation

(y+2)^2 = 9(2x-3).

Re: Finding equation of curve form a point using equal distance

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Originally Posted by

**Blizzardy** Hi guys, need help with this problem please,

A point P(x, y) moves in the x-y plane such that the distance from the line x=3 is always equal to the distance form the point (-6, 2).

Prove that the locus of P can be represented by a curve C with equation

(y+2)^2 = 9(2x-3).

The distance between P(x, y) and the line x = 3 is x - 3.

The distance between P(x, y) and (-6, 2) is $\displaystyle \sqrt{(x+6)^2+(y-2)^2$.

Equate the two and simplify to find the locus of P.