Question

Find the coordinates of focus, axis of the parabola and length of latus rectum x2 =
-16y.

Answer 1

Answer:

The given equation is x

2

=−9y

Here the coefficient of y is negative.

Hence, the parabola opens downwards

On comparing this equation with x

2

=−4ay, we get

−4a=−9

⇒a=

4

9

∴ Coordinates of the focus =(0,−a)=(0,−

4

9

)

Axis of the parabola is the y-axis i.e x=0

Equation of directrix y=a i.e. y=

4

9

Length of latus rectum =4a=9