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 = -8x
On comparing given equation with (1), we have
4a = 8 => a = 2
Now,
Focus : F(-2,0)
Vertex : A(0,0) (at any point A)
Equation of the directrix : x – 2 = 0 or x = 2
Axis: y = 0
Length of latus rectum : 4a = 4 x 2 = 8 units
(ii) y2 = -6x
On comparing given equation with (1), we have
4a = 6 => a = 3/2
Now,
Focus : F(-3/2,0)
Vertex : A(0,0) (at any point A)
Equation of the directrix : x – 3/2 = 0 or x = 3/2 or 2x – 3 = 0
Axis: y = 0
Length of latus rectum : 4a = 4 x 3/2 = 6 units
(iii) 5y2 = -16x
or y2 = -16/5 x
On comparing given equation with (1), we have
4a = 16/5 => a = 4/5
Now,
Focus : F(-4/5,0)
Vertex : A(0,0) (at any point A)
Equation of the directrix : x – 4/5 = 0 or 5x – 4 = 0
Axis: y = 0
Length of latus rectum : 4a = 4 x 4/5 = 16/5 units