Find the standard form of the equation of the parabola with given characteristics and vertex at the origin. Focus (5/2,0)
hello? why does my response not appear?
huh- Well, one more try
Since the vertex is at (0,0) you know the equation will be
x^2 = 4py
or
y^2 = 4px.
Since the focus is also on the x-axis, we have
y^2 = 4px
Since the focus is at (p,0) the equation is
y^2 = 4(5/2)x
or
y^2 = 10x
This can be verified at wolframalpha . com by typing in
parabola y^2 = 4px
oops - I mean
parabola y^2 = 10x
To find the standard form of the equation of a parabola with a given vertex and focus, we can use the formula:
(x - h)^2 = 4p(y - k)
where (h, k) is the vertex and p is the distance between the vertex and the focus.
In this case, the vertex is given as (0, 0), and the focus is given as (5/2, 0). The x-coordinate of the focus represents the distance from the vertex to the focus, so p = 5/2.
Now we can substitute these values into the formula:
(x - 0)^2 = 4(5/2)(y - 0)
Simplifying:
x^2 = 10(y - 0)
x^2 = 10y
Therefore, the standard form of the equation of the parabola with a vertex at the origin and focus at (5/2, 0) is x^2 = 10y.