Unit 10 Review Conic Sections_Answer Key

```Unit 10 Review
Verbal
Graph
Each cable of the Golden Gate Bridge is suspended (in the
shape of a parabola) between two towers that are 1280
meters apart.
The top of each tower is 152 meters above the roadway.
The cables touch the roadway at the midpoint between the
two towers.
A diagram that represents the suspension bridge is shown
below.
Directions: Sketch a diagram of the road on the coordinate
plane below. Label your vertex and two other points on the
parabola.
Standard Form Equation
Directions: Find the standard form equation that models
the horizontal distance of the cable from the center of the
bridge (x) and vertical height (y) of the cables of the bridge.
Communication
1. Find the height of the suspension cables over the
roadway as a distance of 320 meters from the
center of the bridge.
Step 1: Highlight your given information
Opens Up:
x = 320, you need to solve for y.
Vertex: (0, 0)
Point on the bridge: (640, 152) 
x = 640, y = 152
Step 2: Plug in known information into the equation to
solve for your focal length (p).
y = 38, the height of the suspension cables are 38 meters.
2. How far from the center of the bridge is the
suspension cable that has a height of 9.5 meters?
y = 9.5, you need to solve for x.
length. Remember x and y should be unknown.
x = 160, the suspension cable is 160 meters away from the
center of the bridge.
Unit 10 Review
1.
y 2 = -4x
A. Find the vertex, the focus, and the directrix of the parabola.
Vertex: (0,0)
Focus: (-1,0)
Directrix: x=1
B. Find three points on the parabola and sketch its graph.
Three points on the parabola
(-1,2)
(0,0)
(-1,-2)
2.
(y -1)2 = -4(x + 5)
A. Find the vertex, the focus, and the directrix of the parabola.
Vertex: (-5,1)
Focus: (6,1)
Directrix: x= -4
B. Find three points on the parabola and sketch its graph.
Three points on the parabola
(-6,3)
(-5,1)
(-6,-1)
3. Find the equation in standard form of a parabola with a focus (-2, -4) and vertex (-4, -4)
Opens right
p=2
Focal width = 8
Vertex = (-4, -4)
8( x  4)  ( y  4)2
Unit 10 Review
4.
(y -1)2 (x + 2)2
+
=1
25
16
A. Find the center, the vertices, and foci. Is the major axis
horizontal or vertical?
B. Sketch the ellipse.
Center: (-2,1)
Vertices: (-2,6) (-2,-4)
Foci: (-2,4) (-2,-2)
5. Find an equation in standard form for the ellipse that satisfies the given conditions: major axis
endpoints are (-2, -3) and (-2, 7) and the minor axis has a length of 4.
Major axis is 10 (a = 5)
Minor axis is 4 (b = 2)
Center= (-2, 2)
( x  2) 2 ( y  2) 2

1
4
25
6.
( x  4) 2 ( y  6) 2

1
9
16
A. Find the center, vertices, and foci of the
hyperbola and sketch its graph. Is the transverse
axis horizontal or vertical?
Center: (-4,-6)
Vertices: (-7,-6) (-1,-6)
Foci: (-9,-6) (1,-6)
4
3
Asymptotes: y   ( x  4)  6
B. Sketch the hyperbolas. Label the
asymptotes.
Unit 10 Review
7. Find an equation in standard form of a hyperbola with foci (-4, 2) and (2, 2) and transverse axis
endpoints (-3, 2) and (1, 2).
Center= (-1, 2)
a=2
c=3
b=
5
( x  1) 2 ( y  2) 2

1
4
5
8. An arch of a bridge over a highway is semi-elliptical in shape and 60 feet across.
The highest point of the arch is 20 feet above the highway. A truck that is 12 feet 6 inches tall wishes to
pass through the tunnel. If one side of the truck is on the center stripe, what is the maximum width of
the truck that can fit under the arch?
Unit 10 Review
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