Question

If a parabola's focus is at (3, 4) and the directrix is at y = 2, what is the equation representing this parabola?

Answer 1

Given:

$\text{Focus (3,4) ; directrix is y=2}$

$\text{Let (x}_0,y_0)\text{ }be\text{ any point on the parabola}$

$\begin{gathered} \sqrt[]{(x_0-3)^2+(y_0-4)^2}=|y_0-2| \\ (x_0-3)^2+(y_0-4)^2=(y_0-2)^2 \\ x^2_0-6x_0+9+y^2_0-8y_0+16=y^2_0-4y_{\circ}+4 \\ x^2_0-6x_0-4y_0+21=0 \end{gathered}$

Equation of parabola is

$x^2-6x-4y+21=0$