Question

The slope of a chord of the parabola $y^2 = 4ax$ which is normal at one end and which subtends a right angle at the origin is

• A. $\pm\frac{1}{\sqrt{2}}$
• B. $\pm\sqrt{2}$
• C. $\pm\,2$
• D. none of these.

Answer 1

Answer: (B)

The equation of a normal to the parabola, $y^2 = 4ax$
is $tx + y = 2at + at^3$
If the normal chord makes a right angle at the vertex of the parabola, then
$t^2 = 2 $
$\therefore t = \pm \sqrt{2}$
$\therefore $ slope of normal chord is $-t = \pm \sqrt {2}$