Write the equation for a parabola with a focus at (−4,8)(-4,8)(−4,8)left parenthesis, minus, 4, comma, 8, right parenthesis and a directrix at x=−6x=-6x=−6x, equals, minus, 6.

Given:

The focus of the parabola is at (-4,8).

The directrix is at x=-6.

To find:

The equation of the parabola.

Solution:

The directrix is at x=-6, which is a vertical line. So, the parabola is horizontal.

The equation of a horizontal parabola is

Where, (h,k) is vertex, (h+p,k) is focus and x=h-p.

The focus of the parabola is at (-4,8).

            ...(i)

The directrix is at x=-6.

           ...(ii)

Adding (i) and (ii), we get

Putting h=-5 in (i), we get

Putting h=-5, k=8 and p=1 in the standard form of the parabola.

Therefore, the required equation of the parabola is .

step-by-step explanation:

this woman was an important writer and propagandist during the american revolution. she was a member of the committee of correspondence (in fact the committee was formed in her home) and was an advisor to many of the revolutionary leaders, including george washington and john adams. who was this revolutionary woman?

answer: a) (0,0), (1,1), (2,8), and (3,27).

step-by-step explanation:

0^3=0

1^3=1

2^3=8

3^3=27

in effect, the exponential equation for this would me y=3^x. each x-coordinate cubed is giving the y coordinate, so a is your answer : )