Question

If the focus of a parabola is (0, –3) and its directrix is y = 3, then its equation is ______.

Options

• x² = –12y

• x² = 12y

• y² = –12x

• y² = 12x

Answer 1

If the focus of a parabola is (0, –3) and its directrix is y = 3, then its equation is x² = –12y.

Explanation:

According to the definition of parabola

`sqrt((x - 0)^2 + (y + 3)^2) = |(y - 3)/sqrt((0)^2 + (1)^2)|`

⇒ `sqrt(x^2 + y^2 + 9 + 6y) = |y - 3|`

Squaring both sides, we have

x² + y² + 9 + 6y = y² + 9 – 6y

⇒ x² + 9 + 6y = 9 – 6y

⇒ x² = – 12y