Write an equation of a parabola with vertex (2,0) and directrix x=4 . Write your final answer in standard conic form.
The equation of a parabola with vertex (h,k) and directrix x=a is given by:
(y - k)^2 = 4p(x - h)
where p is the distance from the vertex to the focus (and is also the absolute value of the distance from the vertex to the directrix).
Given that the vertex is (2,0) and the directrix is x=4, we can determine that the focus is at (0,0) as it is equidistant from the vertex and the directrix.
The distance from the vertex to the focus is 2, so p = 2.
Therefore, the equation of the parabola in standard conic form is:
(y - 0)^2 = 4(2)(x - 2)
y^2 = 8(x - 2)
y^2 = 8x - 16