2.6.4 Test (TS): Conic Sections Test Archis Chinmulgund Geometry Sem 2 (S3990682) Points possible: 50 Date: ____________ Answer the following questions using what you've learned from this unit. Write your answers in the space provided. Be sure to show all work. CIRCLES 1. Complete the following steps to write the equation of this circle. Part I: Describe the center and radius of the circle. (4 points) The center is at ( 2,4 The radius is 4.5 ). units. Part II: Use the equation below to identify the value of each variable for the circle. (3 points) Standard Form Equation of a Circle (x - h) 2 + (y - v) 2 = r 2 (h, v) = center r = radius length h= 2 v= 4 r = 4.5 Part III: Use Parts I and II to write the standard form equation of the circle. (2 points) 2. Answer the questions about each conic section. Part I: What is the center of the circle having the equation (x - 7) 2 + (y + 2) 2 = 121? What is the radius? (4 points) (7,-2) Center: __________ Radius: __________ 11 Part II: What is the vertex of a parabola having the equation y = -2(x - 5) 2 + 7? Which direction does the parabola open? (3 points) Vertex: ________ -2 Direction of opening: ________ Down Part III: A point on an ellipse is 11 units from one focus and 7 units from the other. What is the length of the major axis? How do you know? (3 points) 3. Fill in the blanks with center, circle, directrix, focus, line, parabola, or radius. A ____________ circle is the set of all points that are equidistant from two points. (1 point) parabola is the set of all points that are equidistant from a given point. The given point is called the A ____________ ____________. the focus The segment showing the distance is called the ____________. (3 points) A ____________ is the set of all points equidistant from a single point and a single line. The single point is called the ____________ and the single line is called the ____________. (3 points) PARABOLAS 4. Use the equation below to complete Parts I, II, and III. Standard Form Equation of a Parabola That Opens Upward y = a(x - h) 2 + v (h, v) = vertex of parabola Part I: A parabola opens upward. The parabola goes through the point (3, -1), and the vertex is at (2, -2). What are the values of h and v? (2 point) h= 2 v= -2 Part II: To find the value of a, subtract the y-coordinate of the vertex from the y-coordinate of the point on the parabola that is 1 unit to the right of the vertex. Find the value of a for the parabola in Part I. Show your work. (3 points) Part III: Use Parts I and II to write the equation of the parabola. (4 points) 5. Find the slope of a line going through each set of points. Then describe the line. Part I: Determine the slope formula by circling your choice. (1 point) Part II: Use your answer from Part I to find the slope of a line going through each set of points. Then describe the line as positive, negative, zero, or undefined. Show your work and explain your answer. A. (5, 7) and (-4, -2) (3 points) B. (1, 3) and (1, -10) (3 points) 6. Raj bought a new super bright flashlight for his camping trip. Use your knowledge of circles and parabolas to define equations that model the beam of light and the reflector within the flashlight. Part I: Raj tested his new flashlight by shining it on his bedroom wall. The beam of light can be described by the equation . How many inches wide is the beam of light on the wall? Step 1: How many inches wide is the beam of light on the wall? Explain your reasoning. (4 points) Step 2: Graph the beam of light on the wall on the coordinate grid below. (4 points) Copyright 2017 Apex Learning Inc. Use of this material is subject to Apex Learning's Terms of Use . Any unauthorized copying, reuse, or redistribution is prohibited. Apex Learning and the Apex Learning Logo are registered trademarks of Apex Learning Inc