Question

The equation of the parabola whose focus is the point (2, 3) and directrix is the line x – 4y + 3 = 0 is ______.

Answer 1

The equation of the parabola whose focus is the point (2, 3) and directrix is the line x – 4y + 3 = 0 is x² + 16y² + 9 – 8xy – 24y + 6x = 0.

Explanation:

Using the definition of parabola,

We have `sqrt((x - 2)^2 + (y - 3)^2) = |(x - 4y + 3)/sqrt(17)|`

Squaring, we get 17(x² + y² – 4x – 6y + 13) = x² + 16y² + 9 – 8xy – 24y + 6x

or 16x² + y² + 8xy – 74x – 78y + 212 = 0