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).