Q66 / 180 · COMEDK 2012 · Mathematics

The parametric equation of a parabola is $x=t^{2}+1, y=2 t+1$. The cartesian equation of its directrix is

  • A
    $y=0$
  • B
    $x=-1$
  • Correct answer
    C
    $x=0$
  • D
    $x-1=0$

Solution

Given that, $x=t^{2}+1 \Rightarrow x-1=t^{2}$ and $\quad y=2 t+1 \Rightarrow y-1=2 t$ Now, $\quad(y-1)^{2}=4 t^{2}=4(x-1)$ $(y-1)^{2}=4(x-1)$ So, $x-1=-1$ $\Rightarrow \quad x=0$

Hence, the correct answer is option: 'C'.

More Parabola Questions