118k views
4 votes
A parabola can be given a focus of 2,0 directrix of x=10, write the equation of the parabola in any form

User Toy
by
7.6k points

1 Answer

2 votes

The equation of the parabola with focus at (2, 0) and directrix x = 10 is:

y^2 = 8(x - 10)

In general, the equation of a parabola with focus at (F, 0) and directrix x = d can be written in two forms:

1. Vertex Form:

y^2 = 4f(x - p)

where:

f is the focal length (distance from the focus to the vertex)

p is the distance from the vertex to the directrix

2. Standard Form:

y^2 = 4ax

where:

a is a constant related to the shape and direction of the parabola

Now, let's apply this to the specific problem:

Given:

Focus: (2, 0)

Directrix: x = 10

Steps:

Identify f and p:

f = 2 (distance from focus to (0, 0))

p = 8 (distance from midpoint between focus and vertex to directrix)

Choose the equation form:

Since the focus is on the x-axis and the directrix is vertical, the parabola opens upwards and the vertex form is suitable.

Substitute values:

y^2 = 4 * 2 * (x - 10)

Therefore, the equation of the parabola is y^2 = 8(x - 10).

User Derrik
by
7.9k points

No related questions found