What is an equation of a parabola with the given vertex and focus?
vertex: (0, 0); focus: (2.5, 0)
(1 point)
Responses
x equals 1 over 4 y squared
Image with alt text: x equals 1 over 4 y squared
y equals 1 over 4 x squared
Image with alt text: y equals 1 over 4 x squared
x equals 1 over 10 y squared
Image with alt text: x equals 1 over 10 y squared
y equals 1 over 10 x squared
The equation of a parabola with the given vertex and focus can be written in the form:
(x-h)^2 = 4p(y-k)
where (h, k) is the vertex and p is the distance from the vertex to the focus.
In this case, the vertex is (0, 0) and the focus is (2.5, 0). Since the focus is to the right of the vertex, the parabola opens to the right. The distance from the vertex to the focus is 2.5 units.
Plugging the values into the equation, we get:
(x-0)^2 = 4(2.5)(y-0)
x^2 = 10y
Therefore, the equation of the parabola with the given vertex and focus is x^2 = 10y.