Question

In the parabola $y^2=4ax,$ the length of the chord passing through the vertex inclined to the axis at $\frac{\pi }{4}$ is

• A. $4a\sqrt{2}$
• B. $2a\sqrt{2}$
• C. $a\sqrt{2}$
• D. $a$

Answer 1

Answer: (A)

Equation of line which is inclined to the axis at
$\frac{\pi }{4}$ is
$y=x$ ..(i)
and equation of parabola is $y^2=4ax$ ..(ii)
From Eqs. (i) and (ii), we get
$x^2-4ax=0$
$\Rightarrow$ $x(x-4a)=0$
$\Rightarrow$ $x=0$ or
$x=4a$
$\therefore$ If $x=0,$ then $y=0$ and if $x=4a,$
then $y=4a$
$\therefore$ Length of the chord OB is
$|OB|=\sqrt{{(4a-0)}^2+{(4a-0)}^2}$
$=\sqrt{16a^2+16a^2}=4a\sqrt{2}$