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:

the answer is thin because within context, the stanza concludes the and frail tone the people have toward each other, and the fact that it would be thin, makes the most sense compared to "pliable" or "not hard or firm to the touch". hope this , good luck.

step-by-step explanation:

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