91Ó°ÊÓ

For the following exercises, graph the parabola, labeling the focus and the directrix. $$y^{2}+2 y-12 x+61=0$$

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

determine the angle \(\theta\) that will eliminate the \(x y\) term and write the corresponding equation without the \(x y\) term. \(16 x^{2}+24 x y+9 y^{2}+6 x-6 y+2=0\)

Write the equation of the ellipse in standard form. Then identify the center, vertices, and foci. $$\frac{(x-2)^{2}}{100}+\frac{(y+3)^{2}}{36}=1$$

Find a polar equation of the conic with focus at the origin, eccentricity of \(e=2,\) and directrix: \(x=3.\)