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  4. If the three normals drawn to the parabola, y 2=2 x pass through the point ( a , 0) a ≠ 0, then 'a' must be greater than :

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Q. If the three normals drawn to the parabola, $y ^{2}=2\,x$ pass through the point $( a , 0) a \neq 0$, then 'a' must be greater than :

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Solution:

For standard parabola For more than 3 normals (on axis)
$x >\frac{ L }{2}$ (where $L$ is length of L.R.)
For $y^{2}=2\,x$
L.R. $=2$
for $(a, 0)$
a $>\frac{\text { L.R. }}{2} \Rightarrow a>1$