Question

In a parabola, if distance between one extremity of latus rectum and foot of perpendicular drawn from other extremity of latus rectum upon directrix is $4\sqrt{5}$, then

• A. distance of focus from directrix will be 4
• B. distance of focus from directrix will be 8
• C. parabola will be equal parabola with $x^2-2x-8y-15=0$
• D. parabola will be equal parabola with $x^2-2x-8y-17=0$

Answer 1

Answer: (A), (C), (D)

From diagram,
$\text{ distance }LM=2a\sqrt{5}=4\sqrt{5}\Rightarrow a=2$
$\therefore$ Distance between focus and directrix $=4$
$LR=8$
P.B. $\Rightarrow x^2-2x-8y-15=0$
$(x-1{)}^2=8(y+2)$
$\therefore$ P.B. is equal parabola with given both parabolas.