Find the vertex, focus, axis, diectrix x and latus rectum of the parabola.

(a) y2 = 8x

(b)y2 = -12x

(c) x2 = 4y and

(d) x2 = -16y.

Asked by Topperlearning User | 27th Feb, 2015, 01:28: PM

Expert Answer:

(a) y2 = 8x . It is a right handed parabola 4a = 8, a = 2.

Vertex (0,0)  Focus (2,0)  Axis : y = 0

Directix : x = -2 and length of latus rectum = 4 x 2 = 8.

(b) y2 = -12x. It is a left handed parabola 4a = -12, a = -3

Vertex (0,0) Focus (-3,0) Axis y = 0.

Directix x = 3 and length of latus rectium = |4 x -3| = 12.

(c) x2 = 4y. It is an upward parabola 4a = 4, a = 1.

Vertex (0,0) Focus (0,1) Axis x = 0

Directix y = -1, length of latus rectium = 4 x 1 = 4.

(d) x2 = -16y. It is a downward parabola. 4a = -16, a = -4

Vertex (0,0) Focus (0,-4) Axis x = 0

Driectix y = 4, length of latus rectum = |4x -4| = 16.

Answered by  | 27th Feb, 2015, 03:28: PM