91Ó°ÊÓ

For the following exercises, graph the given ellipses, noting center, vertices, and foci. \(16 x^{2}+64 x+4 y^{2}-8 y+4=0\)

For the following exercises, sketch a graph of the hyperbola, labeling vertices and foci. \(-100 x^{2}+1000 x+y^{2}-10 y-2575=0\)

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

For the following exercises, find the polar equation of the conic with focus at the origin and the given eccentricity and directrix. Directrix: \(x=4 ; \quad e=\frac{1}{5}\)

For the following exercises, graph the parabola, labeling the focus and the directrix. \(-2 x^{2}+8 x-4 y-24=0\)

For the following exercises, find the polar equation of the conic with focus at the origin and the given eccentricity and directrix. Directrix: \(x=-4 ; \quad e=5\)

For the following exercises, graph the given ellipses, noting center, vertices, and foci. \(100 x^{2}+1000 x+y^{2}-10 y+2425=0\)

For the following exercises, sketch a graph of the hyperbola, labeling vertices and foci. \(4 x^{2}+16 x-4 y^{2}+16 y+16=0\)

For the following exercises, graph the equation relative to the \(x^{\prime} y^{\prime}\) system in which the equation has no \(x^{\prime} y^{\prime}\) term. \(21 x^{2}+2 \sqrt{3} x y+19 y^{2}-18=0\)

For the following exercises, graph the given ellipses, noting center, vertices, and foci. \(4 x^{2}+16 x+4 y^{2}+16 y+16=0\)