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).

Identify each equation without completing the square. 100x² - 7y² + 90y - 368 = 0

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

Find the standard form of the equation of each hyperbola satisfying the given conditions. Endpoints of transverse axis: (0, −6), (0, 6); asymptote: y=2x

Find the standard form of the equation of each hyperbola satisfying the given conditions. Center: (4, −2); Focus: (7, −2); vertex: (6, −2)