Question

The equation of tangents to the parabola $y^2=4ax$ at the ends of its latus rectum is

• A. $x-y+a=0$
• B. $x+y+a=0$
• C. $x+y-a=0$
• D. Both (1) and (2)

Answer 1

Answer: (A), (B)

The correct options are
A $x-y+a=0$
B $x+y+a=0$

Take the parabola as $y^2=4an$

now coordinate of its end of latus rectum are $(a,2a);(a,-2a)$

Now tangent at any point $(x^{\prime },y^{\prime })$ on parabola is

$y{y}^{\prime }=2a(n+n^{\prime })$

Tangent at point $(a,2a)$ is $2ay=2an+2aL$

$y=x+a$

$n-y+a=0$

and tangent at point $(a,-2a)$ is $-2ay-2ax+2a2$

$-y=n+a$

$n+y+a=0$

$\therefore n-y+a=0$ and $n+y+a=0$ are equations of tangent.