Question

From a point \((d, 0)\) three normals are drawn to the parabola \(y^{2}=x\) then
(A) \(d=\frac{1}{2}\)
(B) \(d>\frac{1}{2}\)
(C) \(d<\frac{1}{2}\)
(D) \(d=\frac{1}{3}\)

Answer 1

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