Question

8.Focus (0-3); directrix y-3

Answer 1

The given focus of parabola is ( 0,−3 ) and equation of directrix is

y=3 (1)

Since the focus lies on the y axis, the equation of the parabola is either x 2 =4ay or x 2 =−4ay

Also, the directrix, y=3 is above the x axis, while the focus (0,−3) is below the x axis. Hence, the parabola is of the form x 2 =−4ay .

Coordinates of focus are given by

( 0,−a ) (2)

Equation of directrix is given by

y=a (3)

By comparing equation (1),(2) and (3) we get a=3 .

Equation of parabola is x 2 =−4×3×y =−12y

Thus, the equation of the parabola with focus (0,−3) and equation of directrix y=3 is x 2 =−12y .