Chapter 7

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: \((2,4) ;\) Directrix: \(x=-4\)

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: \((-3,4)\); Directrix: \(y=2\)

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: \((7,-1) ;\) Directrix: \(y=-9\)

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

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 \(10 ;\) length of minor axis \(=4\) 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. Major axis vertical with length 20 ; length of minor axis \(=10\); ecenter: \((2,-3)\)

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

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 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 \((9,6)\)

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

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 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 \((5,1)\)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Convert each equation to standard form by completing the square on \(x\) or \(y .\) Then find the vertex, focus, and directrix of the parabola. Finally, graph the parabola. $$x^{2}-2 x-4 y+9=0$$

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

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. \(4 x^{2}-y^{2}+32 x+6 y+39=0\)

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

Convert each equation to standard form by completing the square on \(x\) or \(y .\) Then find the vertex, focus, and directrix of the parabola. Finally, graph the parabola. $$y^{2}-2 y+12 x-35=0$$

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

Convert each equation to standard form by completing the square on \(x\) or \(y .\) Then find the vertex, focus, and directrix of the parabola. Finally, graph the parabola. $$y^{2}-2 y-8 x+1=0$$

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

Convert each equation to standard form by completing the square on \(x\) or \(y .\) Then find the vertex, focus, and directrix of the parabola. Finally, graph the parabola. $$x^{2}+6 x-4 y+1=0$$

Graph each ellipse and give the location of its foci. $$\frac{(x-1)^{2}}{2}+\frac{(y+3)^{2}}{5}=1$$

Convert each equation to standard form by completing the square on \(x\) or \(y .\) Then find the vertex, focus, and directrix of the parabola. Finally, graph the parabola. $$x^{2}+8 x-4 y+8=0$$

Graph each ellipse and give the location of its foci. $$\frac{(x+1)^{2}}{2}+\frac{(y-3)^{2}}{5}=1$$

Use the vertex and the direction in which the parabola opens to determine the relation's domain and range. Is the relation a function? $$y^{2}+6 y-x+5=0$$

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. \(4 x^{2}-25 y^{2}-32 x+164=0\)

Graph each ellipse and give the location of its foci. $$9(x-1)^{2}+4(y+3)^{2}=36$$