Locus Help please (1 Viewer)

[elainess]

If 'R' is the fixed point (3,2) and 'P' is the movable point (x,y)
Find the equation of the locus of 'P' if distance PR is twice the distance from P to y=-1

thankss!

 

[lolokay]

the point on line y=-1 will have coordinates (x, -1)
by the distance formula..
2 sqrt[(y- -1)^2 + (x-x)^2] = sqrt[(y-2)^2 + (x-3)^2]
squaring both sides, and expanding gives
4y^2 + 8y + 4 = y^2 - 4y + 4 + x^2 - 6x + 9
3y^2 + 12y - x^2 + 6x - 9 = 0
or 3y(y+4) - (x-3)^2 = 0