91Ó°ÊÓ

Find the vertices, foci, and asymptotes of the hyperbola, and sketch its graph. \(x^{2}-2 y^{2}=3\)

(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. $$x y+4=0$$

Find the focus, directrix, and focal diameter of the parabola, and sketch its graph. $$x=\frac{1}{2} y^{2}$$

\begin{array}{l}{1-22 \text { a pair of parametric equations is given. }} \\\ {\text { (a) Sketch the curve represented by the parametric equations. }} \\\ {\text { (b) Find a rectangular-coordinate equation for the curve by }} \\\ {\text { eliminating the parameter. }}\end{array} $$ x=\sin ^{2} t, \quad y=\cos t $$

(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. $$x^{2}+2 x y+y^{2}+x-y=0$$

15–22 (a) Find the eccentricity and identify the conic. (b) Sketch the conic and label the vertices. $$r=\frac{4}{1+3 \cos \theta}$$

\begin{array}{l}{1-22 \text { a pair of parametric equations is given. }} \\\ {\text { (a) Sketch the curve represented by the parametric equations. }} \\\ {\text { (b) Find a rectangular-coordinate equation for the curve by }} \\\ {\text { eliminating the parameter. }}\end{array} $$ x=\cos t, \quad y=\cos 2 t $$

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 focus, directrix, and focal diameter of the parabola, and sketch its graph. $$x^{2}+6 y=0$$

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