91Ó°ÊÓ

Graph the hyperbola. Find the center, the lines which contain the transverse and conjugate axes, the vertices, the foci and the equations of the asymptotes. $$ \frac{(x+1)^{2}}{9}-\frac{(y-3)^{2}}{4}=1 $$

Graph the ellipse. Find the center, the lines which contain the major and minor axes, the vertices, the endpoints of the minor axis, the foci and the eccentricity. $$ \frac{(x-1)^{2}}{9}+\frac{(y+3)^{2}}{4}=1 $$

Find the standard equation of the circle and then graph it. Center \(\left(\pi, e^{2}\right),\) radius \(\sqrt[3]{91}\)

Sketch the graph of the given parabola. Find the vertex, focus and directrix. Include the endpoints of the latus rectum in your sketch. $$ (x+2)^{2}=-20(y-5) $$

Graph the ellipse. Find the center, the lines which contain the major and minor axes, the vertices, the endpoints of the minor axis, the foci and the eccentricity. $$ \frac{(x+2)^{2}}{16}+\frac{(y-5)^{2}}{20}=1 $$

Sketch the graph of the given parabola. Find the vertex, focus and directrix. Include the endpoints of the latus rectum in your sketch. $$ (y-4)^{2}=18(x-2) $$

Graph the hyperbola. Find the center, the lines which contain the transverse and conjugate axes, the vertices, the foci and the equations of the asymptotes. $$ \frac{(y+2)^{2}}{16}-\frac{(x-5)^{2}}{20}=1 $$

Complete the square in order to put the equation into standard form. Identify the center and the radius or explain why the equation does not represent a circle. $$ x^{2}-4 x+y^{2}+10 y=-25 $$

Sketch the graph of the given parabola. Find the vertex, focus and directrix. Include the endpoints of the latus rectum in your sketch. $$ \left(y+\frac{3}{2}\right)^{2}=-7\left(x+\frac{9}{2}\right) $$

Graph the hyperbola. Find the center, the lines which contain the transverse and conjugate axes, the vertices, the foci and the equations of the asymptotes. $$ \frac{(x-4)^{2}}{8}-\frac{(y-2)^{2}}{18}=1 $$