Question

Find the equation of a perpendicular dropped from the focus of the parabola $y=-\frac{x^2}{8}$ to straight line which has intercepts of $2$ and $2$ on $x$ and $y$ coordinate axes.

• A. $x+y=2$
• B. $-x+y=2$
• C. $x-y=4$
• D. $x-y=2$

Answer 1

Answer: (D)

$x-y=2$

Equation of the line is
$\frac{x}{2}+\frac{y}{2}=1$ or $x+y=2$ ...(1)
Parabola is $x^2=-8y.$ Its focus is $(0,-2)$
$\therefore p=\frac{2+2}{\sqrt{2}}=2\sqrt{2}.$ Now line $\perp$ to (1) and
passing through $(0,-2)$ is $x-y=2$
Ans: D