FIND THE VERTEX FOCUS AND DIRECTRIX OF THE PARABOLA WORKSHEET

Direction of opening

Opening up

Vertex

(h, k) ==> (3, -4)

Focus

(h, k + a) ==> (3, -4 + 1/4)

(3, -15/4)

Equation of latus rectum

y = k + a

y = -4 + 1/4

= -15/4

Equation of directrix

y = k - a

y = -4 - (1/4)

y = -17/4

Equation of axis of symmetry

x = h

x = 3

Length of latus rectum

4a = 1

1 unit

Direction of opening

Opening up

Vertex

(h, k) ==> (4, 3)

Focus

(h, k + a) ==> (4, 3 + 1/4)

(3, 13/4)

Equation of latus rectum

y = k + a

y = 3 + 1/4

= 13/4

Equation of directrix

y = k - a

y = 3 - (1/4)

y = 11/4

Equation of axis of symmetry

x = h

x = 4

Length of latus rectum

4a = 1 unit

Direction of opening

Opening up

Vertex

(h, k) ==> (1, 0)

Focus

h - a = 1 - (3/4)

= 1 - 3/4

= 1/4

(h - a, k) ==> (1/4, 0)

Equation of latus rectum

x = h - a

x = 1 - 3/4

= 1/4

Equation of directrix

x = h + a

x = 1 + (3/4)

x = 7/4

Equation of axis of symmetry

y = k

y = 0

Length of latus rectum

4a = 3 units

Direction of opening

Opening up

Vertex

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

Focus

h + a = -3 + (1/12)

= -35/12

(h + a, k) ==> (-35/12, -1)

Equation of latus rectum

x = h + a

x = -35/12

Equation of directrix

x = h - a

x = -3 - (1/12)

x = -37/12

Equation of axis of symmetry

y = k

y = -1

Length of latus rectum

4a = 1/3 units

Direction of opening

Opening up

Vertex

(h, k) ==> (-24, 7)

Focus

h + a = -24 + (1/4)

= -95/4

(h + a, k) ==> (-95/4, 7)

Equation of latus rectum

x = h + a

x = -95/4

Equation of directrix

x = h - a

x = -24 - (1/4)

x = -97/4

Equation of axis of symmetry

y = k

y = 7

Length of latus rectum

4a = 1 unit