Exam 10: Conic Sections

Graph the hyperbola. Give the coordinates of the center as well as the values of $a$ and $b$ . - $\frac{(\mathrm{x}-1)^{2}}{4}-(\mathrm{y}-1)^{2}=1$

Solve the problem. -A Ferris wheel has a diameter of 260 feet and the bottom of the Ferris wheel is 11 feet above the ground. How far to the left or right is a car that is 191 feet above the ground? Round to the nearest tenth if necessary.

Solve the problem. -A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 134 feet and a maximum height of 30 feet. Find the height of the arch at 10 feet from its center.

Graph the parabola. State the vertex of the parabola. - $y=-x^{2}-2 x+2$

Find the standard-form equation of the ellipse. -

Graph the hyperbola. Give the coordinates of the center as well as the values of $a$ and $b$ . - $25 x^{2}-9 y^{2}=225$

Find an equation of the circle with the given center and radius. -Center $(0,0)$ , radius 6

Find the equation of the parabola of the form $y=a x^{2}+b x+c$ that passes through the given three points. - $(-2,5),(1,11),(4,35)$

Graph the hyperbola. Give the coordinates of the center as well as the values of $a$ and $b$ . - $36 x^{2}-25 y^{2}-288 x-250 y-949=0$

Find the midpoint of the line segment that connects the given points. - $(7,7)$ and $(4,1)$

Find the center and radius of the circle by completing the square. - $x^{2}+y^{2}-10 x+12 y+49=0$

Solve the problem. -A wildlife researcher is monitoring a black bear that has a radio telemetry collar with a transmitting range of 16 miles. The researcher is in a research station with her receiver and tracking the bear's movements. If we put the origin of a coordinate system at the research station, what is the equation of all possible locations of the bear where the transmitter would be at its maximum range?

Graph the ellipse. Give the coordinates of the center, as well as the values of $a$ and $b$ . - $\frac{x^{2}}{25}+\frac{y^{2}}{4}=1$

Solve. -A one- way street passes under an overpass, which is in the form of the top half of an ellipse, as shown in the figure. Suppose that a truck 34 feet wide passes directly under the overpass. What is the maximum possible height of this truck to the nearest tenth of a foot? Not to scale

Find the center and radius of the circle by completing the square. - $x^{2}+y^{2}-18 x-8 y+72=0$

Graph the circle. State the center and radius of the circle - $(x-4)^{2}+(y-2)^{2}=36$

Solve. -A person at the top of a 600 foot tall building drops a yellow ball. The height of the yellow ball is given by the equation $h=-16 t^{2}+600$ where $h$ is measured in feet and $t$ is the number of seconds since the yellow ball was dropped. A second person, in the same building but on a lower floor that is 408 feet from the ground, drops a white ball 3 seconds after the yellow ball was dropped. The height of the white ball is given by the equation $h=-16(t-3)^{2}+408$ where $h$ is measured in feet and $t$ is the number of seconds since the yellow ball was dropped. Find the time that the balls are the same distance above the ground and find this distance.

Graph the ellipse. Give the coordinates of the center, as well as the values of $a$ and $b$ . - $(\mathrm{x}-1)^{2}+\frac{(\mathrm{y}-2)^{2}}{16}=1$

Graph the hyperbola. Give the coordinates of the center as well as the values of $a$ and $b$ . - $\frac{(x+5)^{2}}{9}-\frac{(y-4)^{2}}{16}=1$

Graph the parabola. State the vertex of the parabola. - $x=(y-6)^{2}-5$