91Ó°ÊÓ

Find the standard equation of the circle and then graph it. Center \((-1,-5),\) radius 10

Sketch the graph of the given parabola. Find the vertex, focus and directrix. Include the endpoints of the latus rectum in your sketch. $$ (x-1)^{2}=4(y+3) $$

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. $$ x^{2}-4 x+y^{2}+10 y=-25 $$

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. $$ \frac{(x-4)^{2}}{8}-\frac{(y-2)^{2}}{18}=1 $$

Put the equation into standard form and identify the vertex, focus and directrix. $$ x^{2}+2 x-8 y+49=0 $$

Put the equation into standard form and identify the vertex, focus and directrix. $$ 3 y^{2}-27 y+4 x+\frac{211}{4}=0 $$

Find the standard form of the equation of the hyperbola which has the given properties. Foci \((0,\pm 8),\) Vertices (0,±5)

Find the standard form of the equation of the ellipse which has the given properties. Foci \((0,\pm 5),\) Vertices (0,±8).

Find the standard form of the equation of the ellipse which has the given properties. Foci (±3,0) , length of the Minor Axis 10

With the help of your classmates show that if \(A x^{2}+C y^{2}+D x+E y+F=0\) determines a non-degenerate conic \(^{11}\) then \- \(A C<0\) means that the graph is a hyperbola \- \(A C=0\) means that the graph is a parabola \- \(A C>0\) means that the graph is an ellipse or circle