Exam 10: Analytic Geometry

Write the word or phrase that best completes each statement or answers the question. -The eccentricity of ellipse A is eA= 0.17 and the eccentricity of ellipse B is eB = 0.82. Which ellipse is flatter?

Choose the equation that matches the graph. -

Fill in the blanks to complete the statement. The graph of $P ( x ) = - 0.8 ( x - 10 ) ^ { 2 } - 3$ is a parabola opening ـــــــــand isـــــــــــ than that of $y = x ^ { 2 }$ .

Solve the problem. -The roof of a building is in the shape of the hyperbola $y ^ { 2 } - 3 x ^ { 2 } = 13$ , where $x$ and $y$ are in meters. Refer to the figure and determine the height, $h$ , of the outside walls. $A = 4 \mathrm {~m}$

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -Explain in your own words how you can tell from the equation whether a parabola opens up or down or whether it opens left or right.

Graph the conic section. - $3 x^{2}+4 y^{2}-36 x+40 y+196=0$

Determine the two equations necessary to graph the ellipse with a graphing calculator. - $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 25 } = 1$

Write an equation for the hyperbola. -vertices at $( 0,7 ) , ( 0 , - 7 )$ ; foci at $( 0,11 ) , ( 0 , - 11 )$

Find the center, foci, and asymptotes of the hyperbola. - $\frac { ( y - 4 ) ^ { 2 } } { 64 } - \frac { ( x + 2 ) ^ { 2 } } { 36 } = 1$

Graph the ellipse. - $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 36 } = 1$

Find the eccentricity of the hyperbola. - $16 x ^ { 2 } - y ^ { 2 } = 1$

Provide an appropriate response. -If an ellipse has vertices at (-4, 0), (4, 0), (0, 9), and (0, -9), what is its domain? What is its range?

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -Suppose that $\mathrm { A } = \mathrm { C } \neq 0$ in the equation $\mathrm { Ax } { } ^ { 2 } + \mathrm { Bx } + \mathrm { Cy } { } ^ { 2 } + \mathrm { Dy } + \mathrm { E } = 0$ . What kind of graph does this equation have?

Determine the two equations necessary to graph the ellipse with a graphing calculator. - $\frac { x ^ { 2 } } { 16 } + \frac { ( y - 5 ) ^ { 2 } } { 25 } = 1$

Determine the two equations necessary to graph the hyperbola with a graphing calculator. - $\frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 144 } = 1$

Write an equation for the parabola. -vertex $( 9 , - 4 )$ , focus $( 9,2 )$

Write an equation for the ellipse. -center at origin; length of major axis 14 ; y-intercepts $\pm 4$

Graph the parabola. - $x = ( y + 3 ) ^ { 2 } + 8$

Give the focus, directrix, and axis for the parabola. - $( x + 2 ) ^ { 2 } = 32 y$

Write an equation for the parabola with vertex at the origin. -Focus $\left( 0 , - \frac { 1 } { 17 } \right)$