Q71 / 155 · WBJEE 2021 · Mathematics

From a point $(\mathrm{d}, 0)$ three normals are drawn to the parabola $\mathrm{y}^{2}=\mathrm{x}$ then

  • A
    $\quad \mathrm{d}=\frac{1}{2}$
  • Correct answer
    B
    $\quad \mathrm{d}>\frac{1}{2}$
  • C
    $\quad \mathrm{d} < \frac{1}{2}$
  • D
    $\quad \mathrm{d}=\frac{1}{3}$

Solution

We know for $\mathrm{y}^{2}=4 \mathrm{ax}$, if we draw a normal from $(\mathrm{h}, 0)$ then, condition for three normal is $\mathrm{h}>2 \mathrm{a}$. Now, $y^{2}=x$ $\therefore \quad d>\frac{1}{2}$

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

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