91Ó°ÊÓ

Find the vertices, foci, and eccentricity of the ellipse. Determine the lengths of the major and minor axes, and sketch the graph. $$ 9 x^{2}+4 y^{2}=1 $$

\(15-28=(a)\) Use the discriminant to determine whether the graph of the equation is a parabola, an ellipse, or a hyperbola. (b) Use a rotation of axes to eliminate the \(x y\) -term. (c) Sketch the graph. $$ 11 x^{2}-24 x y+4 y^{2}+20=0 $$

A polar equation of a conic is given. (a) Show that the conic is a parabola and sketch its graph. (b) Find the vertex and directrix and indicate them on the graph. $$ r=\frac{5}{3+3 \cos \theta} $$

\(11-22\) . Find the focus, directrix, and focal diameter of the parabola, and sketch its graph. $$ x^{2}+6 y=0 $$

Find the vertices, foci, and eccentricity of the ellipse. Determine the lengths of the major and minor axes, and sketch the graph. $$ \frac{1}{2} x^{2}+\frac{1}{8} y^{2}=\frac{1}{4} $$

Find the vertices, foci, and asymptotes of the hyperbola, and sketch its graph. $$ 4 y^{2}-x^{2}=1 $$

\(15-28=(a)\) Use the discriminant to determine whether the graph of the equation is a parabola, an ellipse, or a hyperbola. (b) Use a rotation of axes to eliminate the \(x y\) -term. (c) Sketch the graph. $$ 21 x^{2}+10 \sqrt{3} x y+31 y^{2}=144 $$

\(11-22\) . Find the focus, directrix, and focal diameter of the parabola, and sketch its graph. $$ x-7 y^{2}=0 $$

A polar equation of a conic is given. (a) Show that the conic is a parabola and sketch its graph. (b) Find the vertex and directrix and indicate them on the graph. $$ r=\frac{2}{5-5 \cos \theta} $$

Find the vertices, foci, and asymptotes of the hyperbola, and sketch its graph. $$ 9 x^{2}-16 y^{2}=1 $$