Question

If the chord y=mx+c subtends a right angle at the vertex of the parabola y2=4ax, then the value of c is

Answer 1

$\textit {Conics - (Parabola) }$

Final Answer : c = -4am

Steps:
1) Homogenization :
We have ,
$y^2 = 4ax \\ \\ y = mx + c \\ \\ => 1 = \frac{y-mx}{c}$

2) Now, we will homogenize above equations.
$y^2 = 4ax * \frac{y-mx}{c} \\ \\ => cy^2 -4axy + 4amx^2$

Condition : For given line to subtend, right angle at vertex then
coefficient of $x^2$ + coefficient of $y^2$ = 0
=> c + 4am = 0
$\boxed{\rightarrow c = -4am}$