Question

find the equation of the parabola with:vertex (0,0); focus (0,5)

Explanation:

Step1: Recall the standard form of parabola

For a parabola with vertex \((h,k)\) and focus \((h,k + p)\), the standard form is \((x - h)^2=4p(y - k)\). Here \(h = 0,k = 0\) (vertex \((0,0)\)) and \(k + p=5\) (focus \((0,5)\)), so \(p = 5\).

Step2: Substitute values into the formula

Substitute \(h = 0,k = 0,p = 5\) into \((x - h)^2=4p(y - k)\). We get \(x^{2}=4\times5y\).

Answer:

\(x^{2}=20y\)