Find the solution set for each system by graphing both of the system's equations in the same rectangular coordinate system and finding points of intersection. Check all solutions in both equations.

$\begin{cases} \frac{x^2}{25} + \frac{y^2}{9} = 1 \\ y = 3 \end{cases}$

Find the solution set for each system by graphing both of the system's equations in the same rectangular coordinate system and finding points of intersection. Check all solutions in both equations.

$\begin{cases} 4x^2 + y^2 = 4 \\ 2x - y = 2 \end{cases}$

Graph each semiellipse. y = -√16 - 4x²

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

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)

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

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. $9x^2-4y^2=36$

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.$y=\pm \sqrt{x^2-2}$

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)²/25−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

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

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

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. $4x^2-9y^2-16x+54y-101=0$

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

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

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

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