Question

If vertex of a parabola is (2, –1) and the equation of its directrix is 4x – 3y = 21, then the length of its latus rectum is ______.

Options

• 2

• 8

• 12

• 16

Answer 1

If vertex of a parabola is (2, –1) and the equation of its directrix is 4x – 3y = 21, then the length of its latus rectum is 8.

Explanation:

We are given that directrix of the parabola is 4x – 3y = 21 and vertex of the parabola is (2, –1).

Now a = `|8 + 3 - 21|/5 = 10/5` = 2

∴ Latus rectum of the parabola = 4a = 8