Question

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin.Focus: (0,1/3)

Answer 1

x² = 4y/3

Step-by-step explanation:

The standard form of the parabola is

`(x-h)^2=4p(y-k)`

Where (h, k) is the vertex and p is a number determined by the focus because the focus is located (h, k+p).

In this case, (h, k) = (0, 0), so the focus is also equal to

focus = (0, 1/3) = (0, 0 + p)

It means that

1/3 = 0 + p

1/3 = p

Then, replacing (h, k) = (0, 0) and p = 1/3, we get that the equation of the parabola is

`\begin{gathered} (x-0)^2=4((1)/(3))(y-0) \\ x^2=(4)/(3)y \end{gathered}`

Therefore, the answer is

x² = 4y/3