Question

If $2x+y+\lambda =0$ is a focal chord of the parabola $y^2=-8x$, then the value of $\lambda$ is

• A. $-4$
• B. $4$
• C. $2$
• D. $-2$

Answer 1

Answer: (B)

$4$

$y^2=-8x$

Comparing with general form $(y-k{)}^2=4p(x-h)$

Focus $=(h+p,k)$

$=(-2,0)$

$2x+y+\lambda$ being focal chord passes through focus

$2(-2)+0+\lambda =0$

$\lambda =4$.