The general form of a parabola: y2 = 4ax ….(1)
Focus : F(a,0)
Vertex : A(0,0) (at any point A)
Equation of the directrix : x + a = 0
Axis: y = 0
Length of latus rectum : 4a
(i) y2 = 12x
On comparing given equation with (1), we have
4a = 12 => a = 3
Now,
Focus : F(a,0) = F(3,0)
Vertex : A(0,0)
Equation of the directrix : x + a = 0
=> x + 3 = 0
or x = -3
Axis: y = 0
Length of latus rectum : 4a = 4 x 3 = 12 units
(ii) y2 = 10x
On comparing given equation with (1), we have
4a = 10 => a = 2.5
Now,
Focus : F(a,0) = F(2.5,0)
Vertex : A(0,0)
Equation of the directrix : x + a = 0
=> x + 2.5 = 0
or x = -2.5
Axis: y = 0
Length of latus rectum : 4a = 4 x (2.5) = 10 units
(iii) 3y2 = 8x
or y2 = 8/3 x
On comparing given equation with (1), we have
4a = 8/3 => a = 2/3
Now,
Focus : F(a,0) = F(2/3,0)
Vertex : A(0,0)
Equation of the directrix : x + a = 0
=> x + 2/3 = 0
or x = -2/3
Axis: y = 0
Length of latus rectum : 4a = 4 x 2/3 = 8/3 units