Question

Find the equation of each of the following parabolas

(a) Directrix x = 0, focus at (6, 0) 

(b) Vertex at (0, 4), focus at (0, 2)

(c) Focus at (–1, –2), directrix x – 2y + 3 = 0

Answer 1

We know that the distance of any point on the parabola from its focus and its directrix is same.

(i) Given that, directrix, x = 0 and focus = (6, 0)

So, for any point P(x, y) on the parabola

Distance of P from directrix = Distance of P from focus

 => x² = (x — 6)² + y²

=> y² – 12x + 36 = 0

(ii) Given that, vertex = (0,4) and focus = (0, 2)

Now distance between the vertex and directrix is same as the distance between the vertex and focus.

Directrix is y – 6 = 0

For any point of P(x, y) on the parabola

Distance of P from directrix = Distance of P from focus