Question

A parabola can be drawn given a focus of (8, -1)(8,−1) and a directrix of y=-11y=−11. Write the equation of the parabola in any form.

Answer 1

Answer:

(x - 8)² = 20(y + 6)

Step-by-step explanation:

The focus of the parabola is (8,-1) and the equation of the directrix is y = - 11.

So, the parabola opens up and the axis of symmetry is x = 8 line.

Now, the axis of symmetry and the directrix meet at the point (8,-11).

So, the vertex of the parabola will be the midpoint of (8,-1) and (8,-11) i.e. (8,-6).

Now, half of the distance between the focus and the directrix is = a = $\frac{11 - 1}{2} = 5$ units.

So, the equation of the parabola in vertex form will be

(x - 8)² = 4 × 5 × (y + 6)

⇒ (x - 8)² = 20(y + 6) (Answer)