Parabola Ques 4
- Suppose that the normals drawn at three different points on the parabola $y^2=4 x$ pass through the point $(h, 0)$. Show that $h>2$.
(1981, 4M)
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Answer:
Correct Answer: 4.$(1)$
Solution: If three different normals are drawn from $(h, 0)$ to $y^2=4 x$.
Then, equation of normals are $y=m x-2 m-m^3$ which passes through $(h, 0)$.
$\Rightarrow m h-2 m-m^3=0 \Rightarrow h=2+m^2 $
$\text { where, } 2+m^2 \geq 2$
$\therefore \quad h>2$ [neglect equality as if $2+m^2=2 \Rightarrow m=0$ ]
Therefore, three normals are coincident.
$ \therefore \quad h>2 $
BETA
