91Ó°ÊÓ

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

For the following exercises, find the equations of the asymptotes for each hyperbola. \(9 x^{2}-18 x-16 y^{2}+32 y-151=0\)

For the following exercises, determine the angle \(\theta\) that will eliminate the \(x y\) term and write the corresponding equation without the \(x y\) term. \(x^{2}+4 x y+y^{2}-2 x+1=0\)

For the following exercises, convert the polar equation of a conic section to a rectangular equation. \(r=\frac{6 \sec \theta}{-2+3 \sec \theta}\)

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. \(3 y^{2}-4 x-6 y+23=0\)

For the following exercises, find the equations of the asymptotes for each hyperbola. \(16 y^{2}+96 y-4 x^{2}+16 x+112=0\)

For the following exercises, find the foci for the given ellipses. \(x^{2}+4 y^{2}+4 x+8 y=1\)

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. \(x^{2}+4 x+8 y-4=0\)

For the following exercises, determine the angle \(\theta\) that will eliminate the \(x y\) term and write the corresponding equation without the \(x y\) term. \(4 x^{2}-2 \sqrt{3} x y+6 y^{2}-1=0\)

For the following exercises, convert the polar equation of a conic section to a rectangular equation. \(r=\frac{6 \csc \theta}{3+2 \csc \theta}\)