Question

A parabola can be drawn given a focus of (1, -7) and a directrix of y = 1. Write the

equation of the parabola in any form.

Answer 1

Explanation:

focus (1 , -7) ⇒ a = 1 & b = -7

y = 1 ⇒ c = 1

Equation of parabola :

(x - a)² + (y - b)² = (y - c)²

(X - 1)² + (y + 7)² = (y - 1)²

Now, expand.

x² - 2x + 1 + y² + 2*7*y + 7² = y² - 2*y*1 + 1

x² - 2x + 1 + y² - 14y + 49 = y² - 2y +1

x² - 2x + 1 + y² - 14y + 49 - y² + 2y - 1 = 0

x² - 2x + y² - y² - 14y + 2y + 1 + 49 - 1 = 0

x² - 2x - 12y + 49 = 0