Exam 6: Conic Sections

Find the vertex, focus, and directrix of the parabola. Graph the equation. - $y^{2}+10 y=12 x+23$

Find the center, foci, and vertices of the ellipse. - $4 x ^ { 2 } + 16 y ^ { 2 } = 64$

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola. - $\frac { y ^ { 2 } } { 36 } - \frac { x ^ { 2 } } { 81 } = 1$

Find an equation for the ellipse described. -Center at (0, 0); focus at (-2, 0); vertex at (3, 0)

Find the vertex, focus, and directrix of the parabola with the given equation. - $( x - 4 ) ^ { 2 } = - 20 ( y + 3 )$

Find the equation in standard form of the parabola described. -The vertex has coordinates (5, 6), and the focus has coordinates (5, 3).

Graph the equation. - $( y + 1 ) ^ { 2 } = 7 ( x - 2 )$

Solve the problem. -The roof of a building is in the shape of the hyperbola $y ^ { 2 } - x ^ { 2 } = 20$ , where $x$ and $y$ are in meters. Determine the distance, w, the outside walls are apart, if the height of each wall is 12 meters.

Graph the hyperbola. - $36 y^{2}-4 x^{2}=144$

Find an equation for the hyperbola described. -Vertices at $( 0 , - 8 )$ and $( 0,8 ) ;$ asymptote the line $y = \frac { 4 } { 9 } x$

Graph the equation. - $x^{2}=-18 y$

Convert the equation to the standard form for a hyperbola by completing the square. - $x ^ { 2 } - y ^ { 2 } - 2 x + 4 y - 4 = 0$

Graph the hyperbola. - $25 x^{2}=9 y^{2}+225$

Find the vertex, focus, and directrix of the parabola. Graph the equation. -

Solve the problem. -The roof of a building is in the shape of the hyperbola $y ^ { 2 } - x ^ { 2 } = 28$ , where $x$ and $y$ are in meters. Refer to the figure and determine the height $h$ of the outside walls.

Find the vertex, focus, and directrix of the parabola. Graph the equation. -

Find the center, foci, and vertices of the ellipse. - $36 x ^ { 2 } + 9 y ^ { 2 } = 324$