8. Conic Sections

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)

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)

Use vertices and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. x²/9−y²/25=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. $9y^2-25x^2=225$

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

Use the center, vertices, and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. (x+3)²/25−y²/16=1

Use the center, vertices, and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. (y+2)²/4−(x−1)²/16=1

Find the vertices and locate the foci of each hyperbola with the given equation. Then match each equation to one of the graphs that are shown and labeled (a)–(d).

a. b. c. d.

x²/4−y²/1=1

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

Graph the hyperbola. Locate the foci and find the equations of the asymptotes. 4y^2 - x^2 = 16