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Q.
From a point $(C, 0)$ three normals are drawn to the parabola $y^{2}=x$. Then,
TS EAMCET 2016
Solution:
Given, $y^{2}=x$
$\therefore 4 a=1 $
$\Rightarrow a=\frac{1}{4}$
Any normal to the parabola is
$y=m x-2 \,a m-a m^{3}\,\,\,...(i)$
If it passes through $(C, 0)$, then
$ 0 =m C-\frac{1}{2} m-\frac{m^{3}}{4} \,\,\,\left\{\because a=\frac{1}{4}\right\}$
$\Rightarrow m =0 $ and $ \frac{m^{2}}{4}=C-\frac{1}{2} $
$ \therefore C > \frac{1}{2} $