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 = 16y
On comparing given equation with (1), we have
4a = 16 => a = 4
Now,
Focus : F(0, 4)
Vertex : A(0, 0)
Equation of the directrix : y + 4 = 0
Axis: x = 0
Length of latus rectum : 4a = 4 x 4 = 16 units
(ii) x2 = 10y
On comparing given equation with (1), we have
4a = 10 => a = 2.5
Now,
Focus : F(0, 2.5)
Vertex : A(0, 0)
Equation of the directrix : y + 2.5 = 0
Axis: x = 0
Length of latus rectum : 4a = 4 x 2.5 = 10 units
(iii) 3x2 = 8y
or x2 = 8/3 y
On comparing given equation with (1), we have
4a = 8/3 => a = 2/3
Now,
Focus : F(0, 2/3)
Vertex : A(0, 0)
Equation of the directrix : y + 2/3 = 0 or 3y + 2 = 0
Axis: x = 0
Length of latus rectum : 4a = 4 x 2/3 = 8/3 units