Task 1 H Print Conic Sections Select any conic section (other than a circle). Answer the questions in this task as they relate to the conic section you chose. Question 1 In your own words, define the conic section you chose as a collection of points (loci) on a plane. BIUXX 2 15px V Space used (includes formatting): 0 / 30000 Question 2 Assuming you know the coordinates of the key points (vertex, foci, directrix), explain how to graph the functions of the conic section you chose using your definition of it. BIUXX 2 15px V Space used (includes formatting): 0 / 30000Space used (includes formatting): 0 / 30000 Question 3 Part A Write the standard equation of the conic section you chose with its center or vertex at the origin. Describe the graph. BIUX X 2 15px V VBBY Space used (includes formatting): 0 / 30000 ? Question Part B Use the drawing tool to sketch the graph and label its parts.Unit Activity: Conic Sections 5 of 7 ? Question Part B Use the drawing tool to sketch the graph and label its parts. T Fill: Line: Width: 2 pt v Lines Sy ShapesQuestion 4 Answer the questions in this part of the task based on your understanding of the definition and the standard equation for the conic you chose. Part A Inspect the equation for the type of conic section you chose. What attributes are necessary to graph it? Be sure to include specific points or equations to complete your answer. . parabola: (x - 3)2 = 12(y -2) . ellipse: (2 - 1)2 25 + ( 3 + 1 ) 2 16 = 1 . hyperbola: (z - 2)2 _ (3 -2)2 = 1 acerUnit Activity: Conic Sections 5 of 7 Sa ? Question Print the graph and mark the attributes of the conic for your reference. T Fill: Line: Width: 2 pt v Lines ...&... .. ... .. . . .;...;.. - - 4 . . . 4 . . .. . . i ... - - 1 .. .). - 1 . .. Shapes.Making Predictions B. x | Product Login | Edme x | 4 Latest Earthquakes x | LearnerProgressDeta x | Course Hero x 5 New Tab x New livery//ua/49413289/848601150/aHROCHM6Ly9mMishcHAuZWRtZW50dWOuY29tL 2x/YXJuZXItdWkvc2Vjb25kYXJ5L3VzZXItYXNzaWdubWVudC80OTQxMz140S9sYXVuY2hwyWQVODQ4NjAxMT nit Activity: Conic Sections 6 of 7 [ Save & Exit Task 2 Print Reflective Properties and Applications of Conics Part A Describe the reflective properties of these conic sections: . parabola . ellipse . hyperbola BIUXX Z 15px V Space used (includes formatting): 0 / 30000 Question Part BPart C How does each conic surface inside the telescope affect the path of light? BIUXX , 15px V A VQXMz140S9sYXVuY2hwyWQVODQ4NjAxMTc30 Unit Activity: Matrices 5 of 8 [ Save & Exit Task 1 Print Matrices and Linear Systems of Equations Imagine that as a ball is tossed, its motion is tracked on a coordinate plane. Given only a few of the points that the ball passes through, it is actually possible to determine the equation of the parabola that represents the ball's path through the air. Part A Assume the ball passes through the points (3, 8), (5, 23 ), and (6, 5). Use this data to set up a system of three equations and three unknowns (a, b, and c) that will allow you to find the equation of the parabola. Write the system in the space provided. BIUXX 2 15px V Space used (includes formatting): 0 / 30000 Part B Use matrix manipulation to solve for a, b, and c. Set up a matrix equation for AX = B based on the system of equations you derived in part B where X is a matrix of the variables a, b, and c. Then, use Gauss-Jordan elimination to find the inverse of A. Finally, use your results to write the equation of the parabola. Show your work and final equation in the space provided. BIUXX 2 15px Space used (includes formatting): 0 / 30000 O Jul 12Space used (includes formatting): 0 / 30000 Part C Now that you have determined the equation of the parabola, assume that x represents the number of seconds that have passed since the ball was thrown and determine approximately how long it will take for the ball to hit the ground. BIUXX 15 px v Space used (includes formatting): 0 / 30000 acerLinear Programming Imagine you are trying to maximize the calories you burn in a 60-minute workout you do a few times a week. Running burns 9 calories per minute, aerobics burns 6 calories per minute, and rowing burns 7 calories per minute. You want to perform all three exercises to work different muscle groups. For the best effect, you need to run for at least 5 minutes and row for at least 15 minutes. Your aerobics session should be at least 30 minutes. How many minutes should you perform each exercise to burn the maximum calories? Part A Write a system of inequalities and/or equations based on the given constraints. Then, note the objective function. BIUXX 15px Space used (includes formatting): 0 / 30000 Part B Convert the inequalities into equations, and then use the substitution method to find three possible vertices in the form (x, y, z). BIUXX Z 15px Space used (includes formatting): 0 / 30000 O acerSpace used (includes formatting): 0 / 30000 Part C Test the three possible vertices that you found in the objective function in part A. Use those values to determine which set of values maximizes the objective function. Show your work and final answer in the space provided. BI UX X2 15px Space used (includes formatting): 0 / 30000 acer all page upTask 3 Print Solving Linear Programming Problems Using a Calculator Linear programming problems can also be solved using a graphing calculator. The following instructions will work for most commonly used graphing calculators, but note that they might vary slightly based on calculator model. Graphing Calculator Tip C Now that you've learned how to use a graphing calculator to solve linear programming problems, solve the following problems. Part A 2x + y