Question

Find the co-ordinates of the focus, vertex, equation of the directrix, axis and the length of latus rectum of the parabola 

(a) y² = 20x, 

(b) x² = 8y, 

(c) x² = -16y

Answer 1

(a) y² = 20x 

y² = 4(5)x

∴ a = 5

Vertex	(0,0)	(0,0)
Focus	(a,0)	(5,0)
Axis	x-axis	y = 0
Directrix	x + a = 0	x + 5 = 0
Length of latus rectum	4a	20

(b) x² = 8y = 4(2)y 

∴ a = 2

Vertex	(0,0)	(0,0)
Focus	(0,a)	(0,2)
Axis	y-axis	x = 0
Directrix	y + a = 0	y + 2 = 0
Length of latus rectum	4a	8

(c) x² = -16y = -4(4)y 

∴ a = 4

Vertex	(0,0)	(0,0)
Focus	(0,-a)	(0,-4)
Axis	y-axis	x = 0
Directrix	y - a = 0	y - 4 = 0
Length of latus rectum	4a	16