Mathematics

Rewrite the parabola in standard form by completing the square—this transforms a messy equation into the canonical $(x-h)^2 = 4p(y-k)$ shape. Once you identify the vertex $(h, k)$ and the focal parameter $p$ (which tells you how far the focus sits from the vertex along the axis of symmetry), finding the focus is just one step: it's always at distance $|p|$ from the vertex in the direction the parabola opens.

Rewrite the parabola in standard form by completing the square—this transforms a messy equation into the canonical $(x-h)^2 = 4p(y-k)$ shape. Once you identify the vertex $(h, k)$ and the focal parameter $p$ (which tells you how far the focus sits from the vertex along the axis of symmetry), finding the focus is just one step: it's always at distance $|p|$ from the vertex in the direction the parabola opens.