Chapter 7

In Exercises \(1-18,\) graph each ellipse and locate the foci. $$\frac{x^{2}}{16}+\frac{y^{2}}{4}=1$$

In Exercises \(1-18,\) graph each ellipse and locate the foci. $$\frac{x^{2}}{25}+\frac{y^{2}}{16}=1$$

In Exercises \(1-18,\) graph each ellipse and locate the foci. $$\frac{x^{2}}{9}+\frac{y^{2}}{36}=1$$

In Exercises \(1-18,\) graph each ellipse and locate the foci. $$\frac{x^{2}}{16}+\frac{y^{2}}{49}=1$$

In Exercises \(1-18,\) graph each ellipse and locate the foci. $$\frac{x^{2}}{25}+\frac{y^{2}}{64}=1$$

In Exercises 5-12, find the standard form of the equation of each hyperbola satisfying the given conditions. Foci: \((0,-3),(0,3) ;\) vertices: \((0,-1),(0,1)\)

In Exercises \(1-18,\) graph each ellipse and locate the foci. $$\frac{x^{2}}{49}+\frac{y^{2}}{36}=1$$

Find the focus and directrix of the parabola with the given equation. Then graph the parabola. $$ y^{2}=4 x $$

Find the standard form of the equation of each hyperbola satisfying the given conditions. Foci: \((0,-6),(0,6) ;\) vertices: \((0,-2),(0,2)\)

In Exercises \(1-18,\) graph each ellipse and locate the foci. $$\frac{x^{2}}{49}+\frac{y^{2}}{81}=1$$

Find the focus and directrix of the parabola with the given equation. Then graph the parabola. $$ y^{2}=-8 x $$

Find the standard form of the equation of each hyperbola satisfying the given conditions. Foci: \((-4,0),(4,0) ;\) vertices: \((-3,0),(3,0)\)

In Exercises \(1-18,\) graph each ellipse and locate the foci. $$\frac{x^{2}}{64}+\frac{y^{2}}{100}=1$$

Find the focus and directrix of the parabola with the given equation. Then graph the parabola. $$ y^{2}=-12 x $$

Find the standard form of the equation of each hyperbola satisfying the given conditions. Foci: \((-7,0),(7,0) ;\) vertices: \((-5,0),(5,0)\)

In Exercises \(1-18,\) graph each ellipse and locate the foci. $$\frac{x^{2}}{4}+\frac{y^{2}}{25}=1$$

Find the focus and directrix of the parabola with the given equation. Then graph the parabola. $$ x^{2}=12 y $$

Find the standard form of the equation of each hyperbola satisfying the given conditions. Endpoints of transverse axis: \((0,-6),(0,6)\) asymptote: \(\quad y=2 x\)

In Exercises \(1-18,\) graph each ellipse and locate the foci. $$\frac{x^{2}}{\frac{81}{4}}+\frac{y^{2}}{\frac{25}{16}}=1$$

Find the focus and directrix of the parabola with the given equation. Then graph the parabola. $$ x^{2}=8 y $$

Find the standard form of the equation of each hyperbola satisfying the given conditions. Endpoints of transverse axis: \((-4,0),(4,0)\) asymptote: \(\quad y=2 x\)

In Exercises \(1-18,\) graph each ellipse and locate the foci. $$x^{2}=1-4 y^{2}$$

Find the focus and directrix of the parabola with the given equation. Then graph the parabola. $$ x^{2}=-16 y $$

Find the standard form of the equation of each hyperbola satisfying the given conditions. Center: \((4,-2) ;\) Focus: \((7,-2)\) vertex: \((6,-2)\)

In Exercises \(1-18,\) graph each ellipse and locate the foci. $$4 y^{2}=1-4 x^{2}$$

Find the focus and directrix of the parabola with the given equation. Then graph the parabola. $$ x^{2}=-20 y $$

Find the standard form of the equation of each hyperbola satisfying the given conditions. Center: \((-2,1) ;\) Focus: \((-2,6)\) vertex: \((-2,4)\)

In Exercises \(1-18,\) graph each ellipse and locate the foci. $$25 x^{2}+4 y^{2}=100$$

Find the focus and directrix of the parabola with the given equation. Then graph the parabola. $$ y^{2}-6 x=0 $$

In Exercises 13-26, use vertices and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. $$\frac{x^{2}}{9}-\frac{y^{2}}{25}=1$$

In Exercises \(1-18,\) graph each ellipse and locate the foci. $$9 x^{2}+4 y^{2}=36$$

Find the focus and directrix of the parabola with the given equation. Then graph the parabola. $$ x^{2}-6 y=0 $$

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

In Exercises \(1-18,\) graph each ellipse and locate the foci. $$4 x^{2}+16 y^{2}=64$$

Find the focus and directrix of the parabola with the given equation. Then graph the parabola. $$ 8 x^{2}+4 y=0 $$

Use vertices and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. $$\frac{x^{2}}{100}-\frac{y^{2}}{64}=1$$

In Exercises \(1-18,\) graph each ellipse and locate the foci. $$4 x^{2}+25 y^{2}=100$$

Find the focus and directrix of the parabola with the given equation. Then graph the parabola. $$ 8 y^{2}+4 x=0 $$

Use vertices and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. $$\frac{x^{2}}{144}-\frac{y^{2}}{81}=1$$

In Exercises \(1-18,\) graph each ellipse and locate the foci. $$7 x^{2}=35-5 y^{2}$$

Find the standard form of the equation of each parabola satisfying the given conditions. Focus: \((7,0) ;\) Directrix: \(x=-7\)

Use vertices and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. $$\frac{y^{2}}{16}-\frac{x^{2}}{36}=1$$

In Exercises \(1-18,\) graph each ellipse and locate the foci. $$6 x^{2}=30-5 y^{2}$$

Find the standard form of the equation of each parabola satisfying the given conditions. Focus: \((9,0) ;\) Directrix: \(x=-9\)

Use vertices and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. $$\frac{y^{2}}{25}-\frac{x^{2}}{64}=1$$

Find the standard form of the equation of each parabola satisfying the given conditions. Focus: \((-5,0) ;\) Directrix: \(x=5\)

Use vertices and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. $$4 y^{2}-x^{2}=1$$

Find the standard form of the equation of each parabola satisfying the given conditions. Focus: \((-10,0) ;\) Directrix: \(x=10\)

Use vertices and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. $$9 y^{2}-x^{2}=1$$

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