Question

The equation of the normals at the end points of the latus rectum of the parabola $y^2=8x$ is/are

• A. $x+y+6=0$
• B. $x-y+6=0$
• C. $x-y-6=0$
• D. $x+y-6=0$

Answer 1

Answer: (C), (D)

The correct options are
C $x-y-6=0$
D $x+y-6=0$

The coordinates of the end points of latus rectum for parabola $y^2=8x$ are $(2,4)$ and $(2,-4)$.

The equation of the normal at point $(x_1,y_1)$ on $y^2=4ax$ is
$y-y_1=-\frac{y_1}{2a}(x-x_1)$

For the given parbola $y^2=8x\Rightarrow a=2$
Putting $(x_1,y_1)=(2,4)$ in above equation we get normal equation as
$x+y-6=0$
Similarly, the other equation of the normal at $(2,-4)$ is
$x-y-6=0$