Question
What is an equation of a parabola with the given vertex and focus?
vertex: (0, 0); focus: (2.5, 0)
x = 1/4y^2
y = 1/4x^2
x = 1/10y^2
y = 1/10x^2
vertex: (0, 0); focus: (2.5, 0)
x = 1/4y^2
y = 1/4x^2
x = 1/10y^2
y = 1/10x^2
Answers
GPT 3.5
The equation of a parabola with vertex (h, k) and focus (h + p, k) is given by (x - h)^2 = 4p(y - k) where p is the distance between the vertex and focus.
In this case, the vertex is at (0, 0) and the focus is at (2.5, 0). Therefore, p = 2.5.
Substitute the values of h, k, and p into the equation:
(x - 0)^2 = 4(2.5)(y - 0)
x^2 = 10y
Therefore, the equation of the parabola is x^2 = 10y.
In this case, the vertex is at (0, 0) and the focus is at (2.5, 0). Therefore, p = 2.5.
Substitute the values of h, k, and p into the equation:
(x - 0)^2 = 4(2.5)(y - 0)
x^2 = 10y
Therefore, the equation of the parabola is x^2 = 10y.