Question

If focus of any parabola is (-3,0) and directrix is x + 5 = 0, then its equation will be :

(A) y² = 4(x + 4)

(B) y² + 4x + 16 = 0

(C) y² + 4x = 16

(D) x² = 4(y + 4)

Answer 1

Answer is (A) y² = 4(x + 4)

Let P(x, y) be any point on parabola. By definition of parabola,

Distance between (x, y) and focus (- 3, 0)

= Length of ⊥ drawn from P(x, y) to directrix x + 5 = 0.