Question

If the line $y=mx+a$ meets the parabola $y^2=4ax$ at two points whose abscissas are $x_1$ and $x_2,$ then $x_1+x_2=0$ if

• A. $m=-1$
• B. $m=1$
• C. $m=2$
• D. $m=-\frac{1}{2}$

Answer 1

The correct option is C $m=2$

Given line is $y=mx+a\cdots \left(1\right)$
$y^2=4ax\cdots \left(2\right)$
Substitute $y$ from equation $\left(1\right)$ into equation $\left(2\right)$
$(mx+a{)}^2=4ax$
$\Rightarrow m^2{x}^2+2amx+a^2=4ax$
$\Rightarrow m^2{x}^2+(2am-4a)x+a^2=0$
For $x_1+x_2=0,$
Sum of roots $=0$
$\Rightarrow -\frac{2am-4a}{m^2}=0$
$\Rightarrow 4a-2am=0$
$\Rightarrow m=2$