Question

The parametric equation of a parabola is x = t² + 1, y = 2t + 1. The cartesian form of its directrix is

• A. x = 0
• B. x + 1 = 0
• C. y = 0 `
• D. y = 1

Answer 1

Answer: (A)

x = 0

Answer 2

t² = x – 1, t = $\frac{y - 1}{2}$

⇒ $\left( \frac{\mathbf{y}\mathbf{-}\mathbf{1}}{\mathbf{2}} \right)^{\mathbf{2}}\mathbf{= (x}\mathbf{-}\mathbf{1)}\mathbf{\Rightarrow}\mathbf{(y}\mathbf{-}\mathbf{1}\mathbf{)}^{\mathbf{2}}\mathbf{= 4(x}\mathbf{-}\mathbf{1)}$

∴ The equation directrix is x – 1 = -1 ⇒x = 0.