Question

If the normal at point $(1,2)$ on the parabola $y^2=4x$ meets the parabola again a point $(t^2,2t),$ then the value of $t$ is

• A. $1$
• B. $3$
• C. $-1$
• D. $-3$

Answer 1

The correct option is D $-3$

If the normal at point $P\left(t_1\right)=(a{t}_1^2,2a{t}_1)$ on the parabola $y^2=4ax$ meets the parabola again a point $Q\left(t\right)=(a{t}^2,2at),$ then
$t=-t_1-\frac{2}{t_1}$
For $y^2=4x\Rightarrow a=1$
$P=(1,2)\Rightarrow t_1=1\therefore t=-1-2=-3$