Name______________________________________________ Date _______________ Period ___________ Row__________ Pre Calculus Chapter 9 Test REVIEW Find the standard form of the equation of the ellipse and give the location of its foci.
6) 4x2 + 16y2 = 64 10
1) 10
y
y
5
5 -10 -10
-5
5
-5
y
10
5
-5
5
10 x
-10
-5
-5
-5
-10
-10
8)
10 x
(x - 2)2 (y + 2)2 + =1 16 9 10
4) Foci: (0, -3), (0, 3)
y
y-intercepts: (0, -5), (0, 5) 5
Graph the ellipse and locate the foci. x2 y2 5) + =1 9 4
-10
-5
y
-5 -10
5
-5
5
y
5
Find the standard form of the equation of the ellipse satisfying the given conditions. 3) Foci: (0, -3), (0, 3) vertices: (0, -7), (0, 7)
-10
10 x
Graph the ellipse. (x - 2)2 (y - 1)2 7) + =1 9 16
2)
10
5
-10
-10
-10
10 x
-5
10 x
-5
10
5
5
Find the focus and directrix of the parabola with the given equation. 9) y2 = -36x
10 x
-5
10) -
-10
1
1 2 x =y 28
Use vertices and asymptotes to graph the hyperbola. x2 y2 11) =1 9 25 10
21) y2 + 6y + 3x + 0 = 0 Graph the parabola with the given equation. 22) (y - 1)2 = 7(x + 2)
y
10
5
-10
-5
5
y
5
10 x
-5
-10
-5
5
10 x
-5
-10
-10
Convert the equation to the standard form for a hyperbola by completing the square on x and y. 12) y2 - 9x2 - 4y - 36x - 41 = 0
Eliminate the parameter. Find a rectangular equation for the plane curve defined by the parametric equations. 23) x = t + 4, y = t2
13) 4y2 - 16x2 - 16y + 32x - 64 = 0 Find the location of the center, vertices, and foci for the hyperbola described by the equation. (x + 4)2 (y + 4)2 14) = 1 25 81
24) x = t - 3, y = t2 + 5 Find a set of parametric equations for the rectangular equation. 25) y = x4 - 1
Find the vertices and locate the foci for the hyperbola whose equation is given. x2 y2 15) =1 16 100
Solve the problem. 26) A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 198 feet and a maximum height of 35 feet. Find the height of the arch at 15 feet from its center.
Convert the equation to the standard form for a parabola by completing the square on x or y as appropriate. 16) y2 - 4y - 9x - 14 = 0
27) A reflecting telescope has a parabolic mirror for which the distance from the vertex to the focus is 29 feet. If the distance across the top of the mirror is 66 inches, how deep is the mirror in the center?
Find the vertex, focus, and directrix of the parabola with the given equation. 17) (x - 4)2 = -8(y - 2) Find the location of the center, vertices, and foci for the hyperbola described by the equation. (y + 2)2 (x - 2)2 18) = 1 100 81
28) The arch beneath a bridge is semi-elliptical, a one-way roadway passes under the arch. The width of the roadway is 40 feet and the height of the arch over the center of the roadway is 14 feet. Two trucks plan to use this road. They are both 10 feet wide. Truck 1 has an overall height of 13 feet and Truck 2 has an overall height of 14 feet. Draw a rough sketch of the situation and determine which of the trucks can pass under the bridge.
Find the standard form of the equation of the parabola using the information given. 19) Focus: (0, 5); Directrix: y = -5 Convert the equation to the standard form for a parabola by completing the square on x or y as appropriate. 20) x2 - 4x - 4y - 16 = 0 2
