Examples of Parabolas

5 SOLVED PROBLEMS OF PARABOLA

EXAMPLE#1

Find the focus and the directrix of

The following parbola

y² = 16x

x = 16y²

4p = 16

4        4

p = 4

Focus = (h+4,0) Directrix: y=k – 4

Focus = (4,0) Directrix: x = -4

GRAPH:

EXAMPLE#2

Find the directrix,focus, and vertex of

The parabola

y = ½ x²

(x – h)² = 4p(y – k) Standard Form

1/2 x² = y

x² = 2y

2 = 4p

4    4

p = ½

(x – 0)² = 4(1/2)(y – 0)²

Vertex (0,0) Focus (0,1/2) Directrix: y = -1/2

GRAPH:

EXAMPLE#3

Determine the vertex,focus, and the

Directrix of the parbola from this

Equation and graph

(y – 1)² = 8(x + 5)

Vertex (h,k) = (-5,1)

Focus = 4p = 8

              4      4

p = 2 Focus: (-5+2,1)

Focus: (-3,1)

Directrix: x = - 5 - 2

Directrix: x = -7

GRAPH:

EXAMPLE#4

Determine the diractrix , focus and

The vertex of the parabola and graph

(x – 3)² = 3(y + 1)

Vertex (h,k) = (3,-1)

4p = 3

4      4

Focus (3,-1 + ¾) Focus (3, - ¼)

Directrix: y = 1 – ¾  Directrix: y = -7/4

GRAPH:

EXAMPLE#5

Find the Standard Form of a parabola

from the given directrix and vertex and

graph

Vertex (0,4) Directrix: y = 2

SOLUTION

P = 2

Focus = (0,4+2) Focus (0,6)

(x-h)² = 4p(y-4)

(x-0)² = 4(2)(y – 4)

x² = 8(y – 4)

x² = 8y – 32

y = 1/8 (x² + 32) S.F

GRAPH:

And that's all :)