Question

If the line $y=mx+a$ meets the parabola $y^2=4ax$ at two points whose abscissa are $x_1$ and $x_2,$ then the value of $m$ for which $x_1+x_2=0$ is

Answer 1

Given line is
$y=mx+a\cdots \left(1\right)$
$y^2=4ax\cdots \left(2\right)$

From equation $\left(1\right)$ and equation $\left(2\right)$, we get
$(mx+a{)}^2=4ax$
$\Rightarrow m^2{x}^2+2amx+a^2=4ax$
$\Rightarrow m^2{x}^2+(2am-4a)x+a^2=0$

Now for $x_1+x_2=0,$
Sum of roots $=0$
$\Rightarrow -\frac{2am-4a}{m^2}=0$
$\Rightarrow 4a-2am=0$
Since $a\ne 0,$
$\Rightarrow m=2$