Question

Write the equation of the parabola whose vertex is at (−3,0) and the directrix is x + 5 = 0. 

Answer 1

The general equation of the parabola is (y − k)² = 4a(x − h)
Here, the (h, k) = (−3,0)
Now, the directrix is given by
x = h − a
⇒ −5 = −3 − a                            [∵ x + 5 = 0 ⇒ x = −5]
⇒ a = 2
Hence, the equation is given by
(y − 0)² = 4(2)(x + 3)
⇒ y² = 8 (x + 3)