Question

The parabola (y - 1)² = a(x - 2) passes through the point

(1, -2). The equation of its directrix is

• A. 4x - 9 = 0
• B. 4x + 9 = 0
• C. x - 9 = 0
• D. 4x = 17

Answer 1

Answer: (D)

4x = 17

Answer 2

Since (y – 1)² =a(x=2) passes through the point (1, -2)

(-2-1)² = a(1 – 2) ⇒ a = - 9.

The given parabola is (y – 1)² = -9(x – 2) but the equation of directrix of the parabola (y-β)² = 4a(x-α) is x- α = -a.

∴ The directrix of (y – 1)² = -9(x-α) is (x – α) = $\frac{9}{4}$ ⇒ 4x

= 17.