Respuesta :
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
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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