A parabola can be drawn given a focus of ( - 8,0) and a directrix of y= - 2 What can be said about the parabola?

The equation of the parabola is:

y

=

1

32

x

2

Explanation:

Please notice that we know that the parabola opens upward or downward, because the directrix is a horizontal line:

y

=

−

8

This tells use that the equation of the parabola of the form:

y

=

f

(

x

)

Not

x

=

f

(

y

)

.

Furthermore, we can see that it must open upward, because the y coordinate of the focus is above the directrix.

The vertex has the same x coordinate as the focus:

x

=

0

And its y coordinate is halfway between the focus and the directrix:

y

=

8

−

8

2

=

0

Therefore the vertex is

(

0

,

0

)

Use the vertex form of the equation of a parabola that opens upward or downward:

y

=

a

(

x

−

h

)

2

+

k

where the vertex is the point

(

h

,

k

)

.

Substitute the vertex into the equation:

y

=

a

(

x

−

0

)

2

+

0

Simplify:

y

=

a

x

2

The distance, f, from the vertex to the focus is,

f

=

8

; this allows use to find the value of

a

, using the equation:

a

=

1

4

f

a

=

1

32

The equation of the parabola is:

y

=

1

32

x

2

Step-by-step explanation:

3+x

step-by-step explanation:

answer

step-by-step explanation: