Question

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 3x-4=0.find the louces of the point and identify the conic.

Answer 1

let the point be P(x,y)

√((x-3)^2+y^2) = 1.5(x-4/3)
square both sides
(x-3)^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