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The focus of a parabola is located at (4,0), and the directrix is located at x = –4.

Which equation represents the parabola?

y2 = –x
y2 = x
y2 = –16x
y2 = 16x

Respuesta :

JunhaoZ
The distance between the focus and directrix is, in this case, 8. Since the directrix is at x= something, the parabola opens sideways, and since the directrix is on the left, to the right. In which case, y^2=p(x), where p is 4 times distance of half of distance between directrix and focus, so the answer is y^2=16x
MrRoyal

The equation of the parabola whose focus is located at (4,0), and the directrix is located at x = –4 is y^2 = 16x

What is a parabola?

A parabola is any graph that has a U-shaped curve, and  is in the form of a quadratic function

The given parameters are:

Focus = (4,0)

Directrix: x = -4

The equation of a parabola is represented as:

(y - k)^2 = 4p(x - h)

The vertex is (0,0).

So, we have:

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

Evaluate

y^2 = 4px

The value of p is 4.

So, we have:

y^2 = 4 * 4x

Evaluate

y^2 = 16x

Hence, the equation of the parabola is y^2 = 16x

Read more about parabola equations at:

https://brainly.com/question/1480401

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