12.5 Conic sections in polar coordinates  (Page 5/8)

$r=\frac{4}{1+3\sin \theta }$

$r=\frac{2}{5-3\sin \theta }$

$r=\frac{8}{3-2\cos \theta }$

$r=\frac{3}{2+5\cos \theta }$

$r=\frac{4}{2+2\sin \theta }$

$r=\frac{3}{8-8\cos \theta }$

$r=\frac{2}{6+7\cos \theta }$

$r=\frac{5}{5-11\sin \theta }$

$r(5+2\cos \theta )=6$

$r(2-\cos \theta )=1$

$r(2.5-2.5\sin \theta )=5$

$r=\frac{6\sec \theta }{-2+3\sec \theta }$

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

$r=\frac{5}{2+\cos \theta }$

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

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

$r=\frac{3}{1+2\cos \theta }$

$r=\frac{8}{4-5\cos \theta }$

$r=\frac{3}{4-4\cos \theta }$

$r=\frac{2}{1-\sin \theta }$

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

$r(1+\cos \theta )=5$

$r(3-4\sin \theta )=9$

$r(3-2\sin \theta )=6$

$r(6-4\cos \theta )=5$

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

Directrix: $x=-4;e=5$

Directrix: $y=2;e=2$

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

Directrix: $x=1;e=1$

Directrix: $x=-1;e=1$

Directrix: $x=-\frac{1}{4};e=\frac{7}{2}$

Directrix: $y=\frac{2}{5};e=\frac{7}{2}$

Directrix: $y=4;e=\frac{3}{2}$

Directrix: $x=\mathrm{-2};e=\frac{8}{3}$

Directrix: $x=\mathrm{-5};e=\frac{3}{4}$

Directrix: $y=2;e=2.5$

Directrix: $x=\mathrm{-3};e=\frac{1}{3}$

$xy=2$

$x^2+xy+y^2=4$

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

$16x^2+24xy+9y^2=4$

$2xy+y=1$

$\frac{x^2}{25}+\frac{y^2}{64}=1$

$\frac{{(x-2)}^2}{100}+\frac{{\left(y+3\right)}^2}{36}=1$

$9x^2+y^2+54x-4y+76=0$

$9x^2+36y^2-36x+72y+36=0$

$\frac{x^2}{36}+\frac{y^2}{9}=1$

$\frac{{(x-4)}^2}{25}+\frac{{\left(y+3\right)}^2}{49}=1$

$4x^2+y^2+16x+4y-44=0$

$2x^2+3y^2-20x+12y+38=0$

Center at $\left(0,0\right),$ focus at $\left(3,0\right),$ vertex at $\left(\mathrm{-5},0\right)$

Center at $\left(2,\mathrm{-2}\right),$ vertex at $\left(7,\mathrm{-2}\right),$ focus at $\left(4,\mathrm{-2}\right)$

A whispering gallery is to be constructed such that the foci are located 35 feet from the center. If the length of the gallery is to be 100 feet, what should the height of the ceiling be?

$\frac{x^2}{81}-\frac{y^2}{9}=1$

$\frac{{\left(y+1\right)}^2}{16}-\frac{{\left(x-4\right)}^2}{36}=1$

$9y^2-4x^2+54y-16x+29=0$

$3x^2-y^2-12x-6y-9=0$