91Ó°ÊÓ

For the following exercises, find the equations of the asymptotes for each hyperbola. $$ \frac{(x-3)^{2}}{5^{2}}-\frac{(y+4)^{2}}{2^{2}}=1 $$

For the following exercises, find the foci for the given ellipses. $$ \frac{(x+1)^{2}}{100}+\frac{(y-2)^{2}}{4}=1 $$

Convert the polar equation of a conic section to a rectangular equation. $$ r(2.5-2.5 \sin \theta)=5 $$

For the following exercises, rewrite the given equation in standard form, and then determine the vertex \((V),\) focus \((F),\) and directrix \((d)\) of the parabola. $$ y^{2}-6 y+12 x-3=0 $$

Find the equations of the asymptotes for each hyperbola. \(\frac{(y-3)^{2}}{3^{2}}-\frac{(x+5)^{2}}{6^{2}}=1\)

For the following exercises, identify the conic with a focus at the origin, and then give the directrix and eccentricity. $$ r(2.5-2.5 \sin \theta)=5 $$

For the following exercises, determine the angle ? that will eliminate the xy term and write the corresponding equation without the \(xy\) term. $$x^{2}+4 x y+4 y^{2}+3 x-2=0$$

For the following exercises, convert the polar equation of a conic section to a rectangular equation. $$ r(2.5-2.5 \sin \theta)=5 $$

For the following exercises, find the equations of the asymptotes for each hyperbola. $$ \frac{(y-3)^{2}}{3^{2}}-\frac{(x+5)^{2}}{6^{2}}=1 $$

Convert the polar equation of a conic section to a rectangular equation. $$ r=\frac{6 \sec \theta}{-2+3 \sec \theta} $$