Question

If $x+y+1=0$ touches the parabola $y^2=\lambda x$, then $\lambda$ is equal to.

• A. $2$
• B. $4$
• C. $6$
• D. $8$

Answer 1

The correct option is B $4$

$x+y+1=0$ touches the parabola $y^2=\lambda x$

$x+y+1=0$

$y=-x-1$

eqn. of line $y=mx+c$

$m=-1$ $c=-1$

line $x+y+1=0$ touches the parabola $y^2=\lambda x$

$\therefore$ $c=\frac{a}{m}$

$-1=\frac{a}{-1}$

$a=1$

$y^2=4ax$ $\Rightarrow \lambda =4a$

$\lambda =4$