Question

Focus and directrix of the parabola $ {{x}^{2}}=-8ay $ are

• A. $ (-2a,0) $ and $ x=4 $
• B. $ (0,2a) $ and $ y=-2a $
• C. $ (0,-2a) $ and $ y=2a $
• D. $ [2a,0) $ and $ x=-2a $

Answer 1

Answer: (C)

We know that for the parabola
$ {{x}^{2}}=-4ay, $
Focus is $ (0,-a) $ and directrix is $ y=a $
Now, we have the curve $ {{x}^{2}}=-8ay $
$ \Rightarrow $ $ {{x}^{2}}=-4(2a)y $
$ \therefore $ Focus is $ (0,-2a) $ and directrix is $ y=2a. $