In Exercises 43–50, convert each equation to standard form by completing the square on x and y. Then graph the hyperbola. Locate the foci and find the equations of the asymptotes. $4x^2-25y^2-32x+164=0$

In Exercises 51–56, graph each relation. Use the relation's graph to determine its domain and range. $\frac{x^2}{9}-\frac{y^2}{16}=1$

In Exercises 51–56, graph each relation. Use the relation's graph to determine its domain and range. $\frac{y^2}{16}-\frac{x^2}{9}=1$

Find the standard form of the equation of the hyperbola with vertices (5, −6) and (5, 6), passing through (0, 9).

Describe the hyperbola $\(\frac{\left(x+2\right)^2}{9}\)-\(\frac{\left(y-4\right)^2}{16}\)=1$.

Describe the hyperbola $y^2-\frac{{(x-1)}^2}{4}=1$.

Find the standard form of the equation of the hyperbola satisfying the given conditions. Foci: (-8,0), (8,0); Vertices: (-3,0), (3,0)

Find the standard form of the equation of the hyperbola satisfying the given conditions. Foci: (0,-4), (0,4); Vertices: (0, -2), (0,2)