Question

The equations of the normals at the ends of latus rectum of $y^2=4ax$ are

• A. $x\pm y-3a=0$
• B. $x\pm y+3a=0$
• C. $x\pm y-2a=0$
• D. $x\pm y+2a=0$

Answer 1

The correct option is A $x\pm y-3a=0$

Let $y^2=4ax$ be the standarad equation of a parabola.
Ends of latusrectum are $(a,2a)$ and $(a,-2a)$ where $t=1$ and $t=-1$ respectively.
Equation of a normal through a point $(a{t}^2,2at)$ is $y=-xt+2at+a{t}^3$
$\therefore$ Equation of normal at $t=1$ is $y=-x+3a$ and at $t=-1$ is $y=x-3a$
$\therefore$ Required equations of normals are $x\pm y-3a=0$
Hence, option A.