Exam 11: Analytic Geometry

Write an equation for the hyperbola. -The roof of a building is in the shape of the hyperbola $y ^ { 2 } - x ^ { 2 } = 35$ , where $x$ and $y$ are in meters. Reft to the figure and determine the height $\mathrm { h }$ of the outside walls. $A = 5 \mathrm {~m}$

Write an equation for the ellipse. -foci at $( \pm 9,0 )$ ; $x$ -intercepts $( \pm 15,0 )$

Write an equation for the hyperbola. -foci at $( 8 - 2 \sqrt { 29 } , 9 ) , ( 8 + 2 \sqrt { 29 } , 9 ) ; e = \frac { 2 \sqrt { 29 } } { 10 }$

Give the focus, directrix, and axis for the parabola. - $x ^ { 2 } = 4 y$

Provide an appropriate response. - $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 9 } = 1 \text { opens left and right. }$ The hyperbola with equation

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

Graph the parabola. - $x = y ^ { 2 } - 4 y - 1$

Graph the parabola. - $x=-3 y^{2}+9 y+5$

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $x ^ { 2 } + y ^ { 2 } = 9$

Choose the equation that matches the graph. -

Write an equation for the parabola with vertex at the origin. -Focus $( 6,0 )$

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

Write an equation for the ellipse. -foci at $( 0,11 ) , ( 0 , - 11 )$ , through the point $\left( 1 , \frac { 61 \sqrt { 3599 } } { 60 } \right)$

Provide an appropriate response. -To graph $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 36 } = 1$ on a graphics calculator, we must consider the union of the graphs of the two functions, $y _ { 1 } = 6 \sqrt { \frac { x ^ { 2 } } { 16 } - 1 }$ and $y _ { 2 } = - 6 \sqrt { \frac { x ^ { 2 } } { 16 } - 1 }$ . Using the graph of $y = \frac { x ^ { 2 } } { 16 } - 1$ , explain (a) how the solution set of $\frac { x ^ { 2 } } { 16 } - 1 \geq 0$ can be determined graphically and (b) how it relates to the domain of the hyperbola.

Determine the two equations necessary to graph the horizontal parabola using a graphing calculator. - $x - 4 = ( y - 5 ) ^ { 2 }$

Find the eccentricity e of the ellipse. -A railroad tunnel is shaped like a semi-ellipse. The height of the tunnel at the center is $30 \mathrm { ft }$ and the vertical clearance must be $20 \mathrm { ft }$ at a point $5 \mathrm { ft }$ from the center. Find an equation for the ellipse.

Write an equation for the parabola with vertex at the origin. -Through $( - 8,8 )$ , opening to the left

Give the focus, directrix, and axis for the parabola. - $( x - 1 ) ^ { 2 } = 8 ( y - 2 )$

Find the eccentricity e of the ellipse. -A satellite is to be put into an elliptical orbit around a moon. The moon is a sphere with radius $606 \mathrm {~km}$ . Determine an equation for the ellipse if the distance of the satellite from the surface of moon varies from $308 \mathrm {~km}$ to $988 \mathrm {~km}$ .

Write an equation for the hyperbola. -The roof of a building is in the shape of the hyperbola $y ^ { 2 } - x ^ { 2 } = 35$ , where $x$ and $y$ are in meters. Determine the distance, $w$ , between the outside walls. $\mathrm { A } = 7 \mathrm {~m}$