Find the Center ((x-4)^2)/16-((y-5)^2)/4=1

Simplify each term in the equation in order to set the right side equal to ${\displaystyle 1}$. The standard form of an ellipse or hyperbola requires the right side of the equation be ${\displaystyle 1}$.

This is the form of a hyperbola. Use this form to determine the values used to find vertices and asymptotes of the hyperbola.

Match the values in this hyperbola to those of the standard form. The variable ${\displaystyle h}$ represents the x-offset from the origin, ${\displaystyle k}$ represents the y-offset from origin, ${\displaystyle a}$.

The center of a hyperbola follows the form of ${\displaystyle (h,k)}$. Substitute in the values of ${\displaystyle h}$ and ${\displaystyle k}$.