Question

Find the standard form of the equation of the parabola with a focus at (-7, 0) and a directrix at x = 7.

Answer 1

The parabola directrix at x = 7 and focus at (-7, 0)

The horizontal parabola directrix equation is x = h - p

Therfore, the required parabola is horizontal.

Standard form of horizontal parabola is 

Where Center (h, k ),focus is (h +p, k ) and directrix is x  = h - p

Directrix x = h - p

h - p =  7 -----> (1)

Focus (h + p, k) = (-7, 0)

h + p = - 7 ----> (2)

and k = 0

Add the equations (1) & (2).

2h = 0

h = 0

Substitute h value in equation (2).

0 + p = - 7

p = - 7

Vertex of parabola is (h, k) = (0, 0).

substitute h, k , p values in standard form.

(y-0)^2 =(4)(-7)x

y^2 =-28x

Answer 2

The standard form of the equation of the parabola with a focus at (-7, 0) and a directrix at x = 7 will be -28x².

What is the parabola?

It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.

Let the focus of the parabola is at (a, 0).

Then the equation of the parabola will be given as,

y = 4ax²

The focus of the parabola is at (-7, 0) and a directrix at x = 7.

Compare the focus with (a, 0). Then the value of a will be -7.

Then the equation of the parabola will be

y = 4 · (-7) · x²

y = -28x²

The standard form of the equation of the parabola with a focus at (-7, 0) and a directrix at x = 7 will be -28x².

The graph of the parabola is given below.

The parabola is the downward parabola.

More about the parabola link is given below.

https://brainly.com/question/8495504

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