geometry
posted by Anonymous on .
A point is moving in a plane in such a way that its distance from the point(3,0)is 1.5 times its distance from the straight line 3x4=0.find the louces of the point and identify the conic.

let the point be P(x,y)
√((x3)^2+y^2) = 1.5(x4/3)
square both sides
(x3)^2 + y^2 = (9/4)(x^2  8x/3 + 16/9)
x^2  6x + 9 + y^2 = 9x^2/4  6x + 4
4x^2  24x + 36 + 4y^2 = 9x^2  24x + 16
5x^2  4y^2 = 20
or x^2 /4  y^2 /5 = 1 , which is a hyperbola
check my arithmetic