Question

If $P(-3,2)$ is one end of the focal chord $PQ$ of the parabola $y^2+4x+4y=0$, then the slope of the $PQ$ is

• A. $\frac{-4}{3}$
• B. $2$
• C. $\frac{1}{2}$
• D. $-2$

Answer 1

Answer: (A)

$\frac{-4}{3}$

Parabola: $y^2+4x+4y=0$

$=>{(y+2)}^2=-4(x-1)......\left(1\right)$

here $a=(-1),$ $h=1,$ $k=(-2)$

Focus $S:(-1+1,-2)$

$S:(0,-2)$

Now let focal chord to $\left(i\right)$ be $y=mx+c.......\left(ii\right)$

$\left(ii\right)$ passes through focus, $-2=0+c$

$=>c--2$

equation $\left(ii\right)$ becomes $y=mx-2......\left(iii\right)$

$\left(iii\right)$ passes through given point $P(-3,2)$

$=>2=-3m-2$

$=>m=\frac{-4}{3}$

equation $\left(ii\right)$ becomes, $3y=-4x-6$

$=>$ slope of focal chord is $m=\frac{-4}{3}$.