Chapter 7

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

Find the standard form of the equation of each parabola satisfying the given conditions. Focus: \((0,20) ;\) Directrix: \(y=-20\)

Use vertices and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. $$4 x^{2}-25 y^{2}=100$$

Find the standard form of the equation of each parabola satisfying the given conditions. Focus: \((0,-25) ;\) Directrix: \(y=25\)

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

Find the standard form of the equation of each parabola satisfying the given conditions. Focus: \((0,-15) ;\) Directrix: \(y=15\)

Use vertices and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. $$16 y^{2}-9 x^{2}=144$$

Find the standard form of the equation of each ellipse satisfying the given conditions. $$\text { Foci: }(-5,0),(5,0) ; \text { vertices: }(-8,0),(8,0)$$

Find the standard form of the equation of each ellipse satisfying the given conditions. $$\text { Foci: }(-2,0),(2,0) ; \text { vertices: }(-6,0),(6,0)$$

Find the standard form of the equation of each parabola satisfying the given conditions. Vertex: \((5,-2) ;\) Focus: \((7,-2)\)

Use vertices and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. $$y=\pm \sqrt{x^{2}-3}$$

Find the standard form of the equation of each ellipse satisfying the given conditions. $$\text { Foci: }(0,-4),(0,4) ; \text { vertices: }(0,-7),(0,7)$$

Find the standard form of the equation of each parabola satisfying the given conditions. Focus: \((3,2) ;\) Directrix: \(x=-1\)

Find the standard form of the equation of each ellipse satisfying the given conditions. $$\text { Foci: }(0,-3),(0,3) ; \text { vertices: }(0,-4),(0,4)$$

Find the standard form of the equation of each parabola satisfying the given conditions. Focus: \((2,4) ;\) Directrix: \(x=-4\)

Find the standard form of the equation of each ellipse satisfying the given conditions. Foci: \((-2,0),(2,0) ; y\) -intercepts: \(-3\) and 3

Find the standard form of the equation of each parabola satisfying the given conditions. Focus: \((2,4) ;\) Directrix: \(x=-4\)

Find the standard form of the equation of each ellipse satisfying the given conditions. Foci: \((0,-2),(0,2) ; x\) -intercepts: \(-2\) and 2

Find the standard form of the equation of each parabola satisfying the given conditions. Focus: \((7,-1) ;\) Directrix: \(y=-9\)

Find the standard form of the equation of each ellipse satisfying the given conditions. Major axis horizontal with length \(8 ;\) length of minor axis \(=4 ;\) center: \((0,0)\)

Find the standard form of the equation of each ellipse satisfying the given conditions. Major axis horizontal with length \(12 ;\) length of minor axis \(=6 ;\) center: \((0,0)\)

Find the standard form of the equation of each ellipse satisfying the given conditions. Major axis vertical with length \(10 ;\) length of minor axis \(=4 ;\) center: \((-2,3)\)

In Exercises 33-42, use the center, vertices, and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. $$\frac{(x+4)^{2}}{9}-\frac{(y+3)^{2}}{16}=1$$

Find the standard form of the equation of each ellipse satisfying the given conditions. Major axis vertical with length \(20 ;\) length of minor axis \(=10 ;\) center: \((2,-3)\)

Use the center, vertices, and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. $$\frac{(x+2)^{2}}{9}-\frac{(y-1)^{2}}{25}=1$$

Find the standard form of the equation of each ellipse satisfying the given conditions. Endpoints of major axis: \((7,9)\) and \((7,3)\) Endpoints of minor axis: \((5,6)\) and \((9,6)\)

Use the center, vertices, and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. $$\frac{(x+3)^{2}}{25}-\frac{y^{2}}{16}=1$$

Find the vertex, focus, and directrix of each parabola with the given equation. Then graph the parabola. $$ (x-2)^{2}=8(y-1) $$

Find the standard form of the equation of each ellipse satisfying the given conditions. Endpoints of major axis: \((2,2)\) and \((8,2)\) Endpoints of minor axis: \((5,3)\) and \((5,1)\)

Use the center, vertices, and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. $$\frac{(x+2)^{2}}{9}-\frac{y^{2}}{25}=1$$

Find the vertex, focus, and directrix of each parabola with the given equation. Then graph the parabola. $$ (x+2)^{2}=4(y+1) $$

Graph each ellipse and give the location of its foci. $$\frac{(x-2)^{2}}{9}+\frac{(y-1)^{2}}{4}=1$$

Use the center, vertices, and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. $$\frac{(y+2)^{2}}{4}-\frac{(x-1)^{2}}{16}=1$$

Find the vertex, focus, and directrix of each parabola with the given equation. Then graph the parabola. $$ (x+1)^{2}=-8(y+1) $$

Graph each ellipse and give the location of its foci. $$\frac{(x-1)^{2}}{16}+\frac{(y+2)^{2}}{9}=1$$

Use the center, vertices, and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. $$\frac{(y-2)^{2}}{36}-\frac{(x+1)^{2}}{49}=1$$

Find the vertex, focus, and directrix of each parabola with the given equation. Then graph the parabola. $$ (x+2)^{2}=-8(y+2) $$

Graph each ellipse and give the location of its foci. $$(x+3)^{2}+4(y-2)^{2}=16$$

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

Find the vertex, focus, and directrix of each parabola with the given equation. Then graph the parabola. $$ (y+3)^{2}=12(x+1) $$

Graph each ellipse and give the location of its foci. $$(x-3)^{2}+9(y+2)^{2}=18$$

Use the center, vertices, and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. $$(x+3)^{2}-9(y-4)^{2}=9$$

Find the vertex, focus, and directrix of each parabola with the given equation. Then graph the parabola. $$ (y+4)^{2}=12(x+2) $$

Graph each ellipse and give the location of its foci. $$\frac{(x-4)^{2}}{9}+\frac{(y+2)^{2}}{25}=1$$

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 vertex, focus, and directrix of each parabola with the given equation. Then graph the parabola. $$ (y+1)^{2}=-8 x $$

Graph each ellipse and give the location of its foci. $$\frac{(x-3)^{2}}{9}+\frac{(y+1)^{2}}{16}=1$$

Use the center, vertices, and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. $$(y-2)^{2}-(x+3)^{2}=5$$

Find the vertex, focus, and directrix of each parabola with the given equation. Then graph the parabola. $$ (y-1)^{2}=-8 x $$

Graph each ellipse and give the location of its foci. $$\frac{x^{2}}{25}+\frac{(y-2)^{2}}{36}=1$$