8. Conic Sections

Graph the hyperbola. Locate the foci and find the equations of the asymptotes. ((x-2)^2)/25 - ((y+3)^2)/16 = 1

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).

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.

y²/4−x²/1=1

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 each hyperbola satisfying the given conditions. Foci: (−4, 0), (4, 0); vertices:(−3, 0), (3, 0)

Use vertices and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. y²/16−x²/36=1

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

Find the standard form of the equation of each hyperbola.

Find the standard form of the equation of each hyperbola.

Use the center, vertices, and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. (x+4)²/9−(y+3)²/16=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

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

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. $x^2-y^2-2x-4y-4=0$