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A parabola has a vertex at the origin. The focus of the parabola is located at (–2,0).
Which is the equation for the directrix related to the parabola?

y=2
x=2
y=-2
x=-2

Respuesta :

metchelle
Based on the given, it can be said that the parabola is opening to the left since the focus is located at point (-2,0). Based on the basic property of the parabola, the distance between the vertex and the focus is equal to the distance from the vertex to the point where the directrix passes through. Also, the directrix is always parallel to the latus rectum. Therefore, equation of directrix, x=2

Parabola with vertex at origin and focus (-2,0) has equation of directrix related to parabola is,

[tex]x=2[/tex]

How to find the directrix of the parabola?

The directrix of the parabola is the perpendicular to the axis of the parabola. In a parabola the fixed line is called the directrix of the parabola.

In a parabola the fixed point is called the focus of the parabola. It can be given as,

[tex]x=(-a,0)[/tex]

Where [tex]a[/tex] is the directrix of the parabola.

The equation of the directrix can be given as,

[tex]x=a[/tex]

Given information-

The vertex of the parabola is at the origin.

The focus of the parabola is located at (–2,0).

The focus of the parabola is (-2,0) which is the fixed point.

Compare it with the above equation, we get,

[tex]x=2[/tex]

Hence the equation of the directrix related to parabola is,

[tex]x=2[/tex]

Thus, the option 2 is correct option.

Learn more about the directrix of parabola here;

https://brainly.com/question/4148030

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