8. Conic Sections

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. Center: (4, −2); Focus: (7, −2); vertex: (6, −2)

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

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. $16x^2-y^2+64x-2y+67=0$

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

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

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

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

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

Find the standard form of the equation of each hyperbola.

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. $4x^2-25y^2-32x+164=0$

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

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

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