Question

if a normal chord of $y^2=4ax$ subtends an angle $\pi /2$ at the parabola then it's slope can be equal to

• A. $\sqrt{2}$
• B. $-\sqrt{2}$
• C. $1$
• D. $-1$

Answer 1

The correct option is B $-\sqrt{2}$

$y^2=4ax$

Let point of the chord $=(a{t}_1^2,2a{t}_1)$ & $(a{t}_2^2,2a{t}_2)$

Normal to parabola so $t_2=-t_1\frac{-2}{t_1}$

equation of normal parabola-

$y=-tx+2at+a{t}^3$

$\frac{2a{t}_1-0}{a{t}_1^2-0}\left\{\frac{2a{t}_1-0}{a{t}_1^2-0}\right\}=-1$

$t_1{t}_2=-4$

$t_1\left(t_1\frac{-2}{t_1}\right)=-4$

$t_1=\sqrt{2}$