8. Conic Sections

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

Use the center, vertices, and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. (x−3)²−4(y+3)²=4

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

In Exercises 13–26, use vertices and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. x²/100−y²/64=1

Use vertices and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. 4y²−x²=1

Find the standard form of the equation of each hyperbola.

Explain why it is not possible for a hyperbola to have foci at (0,-2) and (0,2) and vertices at (0,-3) and (0,3).

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

Graph the hyperbola. Locate the foci and find the equations of the asymptotes. (x^2)/16 - y^2 = 1

Use vertices and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. $9x^2-4y^2=36$

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. Foci: (0, −3), (0, 3) ; vertices: (0, −1), (0, 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)

Use vertices and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes.$y=\pm \sqrt{x^2-2}$

Find the standard form of the equation of each hyperbola satisfying the given conditions. Foci: (−4, 0), (4, 0); vertices:(−3, 0), (3, 0)