Question

Find the equation Ax^2 + By^2 + Dx + Ey + F = 0 and gives a parametrization of the hyperbola defined by the set of points P that its distance from the point (6, 0) is the three times its distance to the line 3x + 2 = 0.

Answer 1

$\sqrt{(x-6)^2+(y-0)^2}=3\times \left | \frac{3x+2}{3} \right |=|3x+2|$

Squaring both/ sides we ge/t

(х – 6)2 + ? = 3х + 2

So we get

$x^2+y^2-15x-38=0$ is the required equation