Unit 10 Review Link Sheet Answer Key: Real World Applications of Conic Sections 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. Step 3: Create your model using your vertex and focal 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 Review Answer Key: Unit 10 Conic Sections 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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