7.5 Conic sections  (Page 10/23)

Focus $\left(4,0\right)$ and directrix $x=\mathrm{-4}$

Focus $\left(0,\mathrm{-3}\right)$ and directrix $y=3$

Focus $\left(0,0.5\right)$ and directrix $y=\mathrm{-0.5}$

Focus $\left(2,3\right)$ and directrix $x=\mathrm{-2}$

Focus $\left(0,2\right)$ and directrix $y=4$

Focus $\left(\mathrm{-1},4\right)$ and directrix $x=5$

Focus $\left(\mathrm{-3},5\right)$ and directrix $y=1$

Focus $\left(\frac{5}{2},\mathrm{-4}\right)$ and directrix $x=\frac{7}{2}$

Endpoints of major axis at $\left(4,0\right),\left(\mathrm{-4},0\right)$ and foci located at $\left(2,0\right),\left(\mathrm{-2},0\right)$

Endpoints of major axis at $\left(0,5\right),\left(0,\mathrm{-5}\right)$ and foci located at $\left(0,3\right),\left(0,\mathrm{-3}\right)$

Endpoints of major axis at $\left(0,2\right),\left(0,\mathrm{-2}\right)$ and foci located at $\left(3,0\right),\left(\mathrm{-3},0\right)$

Endpoints of major axis at $\left(\mathrm{-3},3\right),\left(7,3\right)$ and foci located at $\left(\mathrm{-2},3\right),\left(6,3\right)$

Endpoints of major axis at $\left(\mathrm{-3},5\right),\left(\mathrm{-3},\mathrm{-3}\right)$ and foci located at $\left(\mathrm{-3},3\right),\left(\mathrm{-3},\mathrm{-1}\right)$

Endpoints of major axis at $\left(0,0\right),\left(0,4\right)$ and foci located at $\left(5,2\right),\left(\mathrm{-5},2\right)$

Foci located at $\left(2,0\right),\left(\mathrm{-2},0\right)$ and eccentricity of $\frac{1}{2}$

Foci located at $\left(0,\mathrm{-3}\right),\left(0,3\right)$ and eccentricity of $\frac{3}{4}$

Vertices located at $\left(5,0\right),\left(\mathrm{-5},0\right)$ and foci located at $\left(6,0\right),\left(\mathrm{-6},0\right)$

Vertices located at $\left(0,2\right),\left(0,\mathrm{-2}\right)$ and foci located at $\left(0,3\right),\left(0,\mathrm{-3}\right)$

Endpoints of the conjugate axis located at $\left(0,3\right),\left(0,\mathrm{-3}\right)$ and foci located $\left(4,0\right),\left(\mathrm{-4},0\right)$

Vertices located at $\left(0,1\right),\left(6,1\right)$ and focus located at $\left(8,1\right)$

Vertices located at $\left(\mathrm{-2},0\right),\left(\mathrm{-2},\mathrm{-4}\right)$ and focus located at $\left(\mathrm{-2},\mathrm{-8}\right)$

Endpoints of the conjugate axis located at $\left(3,2\right),\left(3,4\right)$ and focus located at $\left(3,7\right)$

Foci located at $\left(6,\mathrm{-0}\right),\left(6,0\right)$ and eccentricity of 3

$\left(0,10\right),\left(0,\mathrm{-10}\right)$ and eccentricity of 2.5

$r=\frac{\mathrm{-1}}{1+\text{cos}\theta }$

$r=\frac{8}{2-\text{sin}\theta }$

$r=\frac{5}{2+\text{sin}\theta }$

$r=\frac{5}{\mathrm{-1}+2\text{sin}\theta }$

$r=\frac{3}{2-6\text{sin}\theta }$

$r=\frac{3}{\mathrm{-4}+3\text{sin}\theta }$

$\text{Directrix:}x=4;e=\frac{1}{5}$

$\text{Directrix:}x=\mathrm{-4};e=5$

$\text{Directrix: y}=2;e=2$

$\text{Directrix: y}=\mathrm{-2};e=\frac{1}{2}$

$r=\frac{1}{1+\text{sin}\theta }$

$r=\frac{1}{1-\text{cos}\theta }$

$r=\frac{4}{1+\text{cos}\theta }$

$r=\frac{10}{5+4\text{sin}\theta }$

$r=\frac{15}{3-2\text{cos}\theta }$

$r=\frac{32}{3+5\text{sin}\theta }$

$r(2+\text{sin}\theta )=4$

$r=\frac{3}{2+6\text{sin}\theta }$

$r=\frac{3}{\mathrm{-4}+2\text{sin}\theta }$

$\begin{array}{c}\frac{x^2}{9}+\frac{y^2}{4}=1\hfill \\ \hfill \end{array}$

$\frac{x^2}{4}+\frac{y^2}{16}=1$

$4x^2+9y^2=36$

$25x^2-4y^2=100$

$\frac{x^2}{16}-\frac{y^2}{9}=1$

$x^2=12y$

$y^2=20x$

$12x=5y^2$

$xy=4$

$x^2+4xy-2y^2-6=0$

$x^2+2\sqrt{3}xy+3y^2-6=0$

$x^2-xy+y^2-2=0$

$34x^2-24xy+41y^2-25=0$

$52x^2-72xy+73y^2+40x+30y-75=0$

The mirror in an automobile headlight has a parabolic cross section, with the lightbulb at the focus. On a schematic, the equation of the parabola is given as $x^2=4y.$ At what coordinates should you place the lightbulb?

A satellite dish is shaped like a paraboloid of revolution. The receiver is to be located at the focus. If the dish is 12 feet across at its opening and 4 feet deep at its center, where should the receiver be placed?

Consider the satellite dish of the preceding problem. If the dish is 8 feet across at the opening and 2 feet deep, where should we place the receiver?