The general form of a parabola: x2 = -4ay ….(1)
Focus : F(0, -a)
Vertex : A(0,0) (at any point A)
Equation of the directrix : y – a = 0
Axis: x = 0
Length of latus rectum : 4a
(i) x2 = -8y
On comparing given equation with (1), we have
4a = 8 => a = 2
Now,
Focus : F(0, -2)
Vertex : A(0, 0)
Equation of the directrix : y – 2 = 0
Axis: x = 0
Length of latus rectum : 4a = 4 x 2 = 8 units
(ii) x2 = -18y
On comparing given equation with (1), we have
4a = 18 => a = 9/2
Now,
Focus : F(0, -9/2)
Vertex : A(0, 0)
Equation of the directrix : y – 9/2 = 0 or 2y – 9 = 0
Axis: x = 0
Length of latus rectum : 4a = 4 x 9/2 = 18 units
(iii) 3x2 = -16y
Or x2 = -16/3 y
On comparing given equation with (1), we have
4a = 16/3 => a = 4/3
Now,
Focus : F(0, -4/3)
Vertex : A(0, 0)
Equation of the directrix : y – 4/3 = 0 or 3y – 4 = 0
Axis: x = 0
Length of latus rectum : 4a = 4 x 4/3 = 16/3 units