Focus and directrix of the parabola x2=-8ay are

Question

Focus and directrix of the parabola x2=-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

Tardigrade Admin · Accepted Answer

We know that for the parabola x2=-4ay, Focus is (0,-a) and directrix is y=a Now, we have the curve x2=-8ay ⇒ x2=-4(2a)y ∴ Focus is (0,-2a) and directrix is y=2a.

Q. Focus and directrix of the parabola $x^{2} = - 8 a y$ are

$(- 2 a, 0)$ and $x = 4$

$(0, 2 a)$ and $y = - 2 a$

$(0, - 2 a)$ and $y = 2 a$

$[2 a, 0)$ and $x = - 2 a$

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

Q. Focus and directrix of the parabola x2=−8ay are

(−2a,0) and x=4

(0,2a) and y=−2a

(0,−2a) and y=2a

[2a,0) and x=−2a