Let F(x_{1}, y_{1}) be the focus, lx + my + n = 0, the equation of the directrix and e the eccentricity of the conic. Let P(x, y) be any point on the conic.

FP/PM = e

FP^{2} = e^{2} × PM^{2}

Simplifying this, you get an equation of second degree in x and y of the form

**Ax ^{2} + Bxy + Cy^{2} + Dx + Ey + F = 0**