SCORE: DATE: 28 June 2011NAME: CLASS TIME yCLASS ID: M5 1PS1 – Conics E FOUR SECTIONS, ONE DESTINY L ECLIPSE: (5 points) TOY STORY: (10 points)1. 1. 6. E 2. 2. 7. M 3. 3. 8. E x4. 4. 9. 5. 5. 10. N T KILLERS: (10 points) KARATE KID: (15 points) 1. 1. A 2. 2. 3. 3. R 4. 4. Y 5. 5. ANALYSIS Math 5 Problem Set 1 SY 2011-2012A-TEAM: (5 points) SHREK: (3 points) Conics INSTRUCTIONS: PARABOLA This is a 48–point mental exercise. HPS: 48 / 45 Use the answer sheet for your final answers in simplest form. Use blue or black ball pen for your final answers. ELLIPSE Non-compliance with the instructions will automatically mean a grade of zero. HYPERBOLA
4. What is the orientation of the ellipse whose major axis is vertical?M5 1PS1 5. Locate the coordinates of the intersection of the asymptotes of the hyperbolaECLIPSE : It all begins…with a choice. y 12 x 2 2 1 ?Write the CAPITAL LETTER that corresponds to the correct answer. (1 pt each) 6. What is the length of the transverse axis of an equilateral hyperbola whose conjugate axis has1. Which of the corresponding parts of an ellipse is farthest from its center? endpoints at (– 1, 5) and (– 1, –1)?M. directrix A. extremity T. latus rectum H. vertex 7. If the quotient of the eccentricities of a hyperbola and a parabola is 2/3, what is the product?2. A satellite dish is in the form of a paraboloid ( a 3D figure formed by rotating a parabola 2 2 about its axis). Its receiver is located at the focus which is 25cm from the vertex of the y x paraboloid. If the dish is 9cm deep at the center, what is the area of its circular rim? 8. What is the length of the conjugate axis of the hyperbola 1 ? 25 144M. 900 sq.cm. A. 225 sq.cm. T. 60 sq.cm. H. 25 sq.cm. 9. What is the distance between the focus and the directrix of a parabola whose latus rectum is 23. If an ellipse and a parabola share a focus and corresponding vertex, which of these is true? units long?M. The parabola has a shorter latus rectum. T. The length of LR of the conics are equal. x 3 2 y 4 2A. The ellipse has a shorter latus rectum. H. The lengths of LR cannot be compared. 10. Find an equation of the principal axis of the conic 1. 9 164. The lines y 5 x are asymptotes of a hyperbola whose foci are 26 units apart. Which 12CANNOT be a vertex of the hyperbola?M. (– 12, 0) A. (0, 5) T. (0, – 12) H. (12, 0) KILLERS: …give it your best shot. Write the most appropriate answer in simplest form. (2 pts each; no partial points)5. What type of hyperbola is 9x 2 16y 2 54x 32y 209 0 ? 1. An ellipse with eccentricity 1 has major axis of length 2. How long is its minor axis? 2M. degenerate A. equilateral T. horizontal H. vertical 2. What is the general equation of the asymptote with a positive slope of the hyperbolaTOY STORY: No toy gets left behind. x 2 y 2 2x 2y 1 0 ?Write the most appropriate answer in simplest form. (1 pt each)1. Name the type of conic formed by the intersection of a right circular cone and a plane 3. If the distance between an endpoint of the latus rectum to the vertex of a parabola parallel to exactly two generators of the cone. is 80, then what is the length of the latus rectum?2. Identify the set of points in a plane the sum of whose distances from two fixed points is a 4. What is the graph of x 2 y 2 2x 6y 14 0 ?constant. 5. What is the standard equation of the ellipse with center at (2, – 1), focus at (– 3, – 1) and 23. The graph of y y 2 0 is a degenerate form of what conic? covertex at (2, 11)?
KARATE KID: Sometimes the most important fights are the ones you avoid.Write the most appropriate answer in simplest form. (3 pts each; no partial points)1. A conic has the lines y = – 3 and y = 5 as directrices and the point (1, 26) as a focus. What arethe coordinates of the vertex closest to the given focus? 22. A ball is thrown from the ground and moves along a parabolic path s(t) 16t 32twhere s(t) meters is the vertical displacement in t seconds. At what time, in seconds, will the ballreach maximum height?3. What are the coordinates of the endpoint of a latus rectum of an ellipse with an extremity at(5, 0), vertex at (0,4) that is closest to the origin? The coverage of the first long test on the last meeting next week is CONIC SECTIONS.4. A semi-elliptical tunnel is 10 feet across and 4 feet high. How high is the ceiling 3 feet TCWAG6: Chapter 10 OR TC7: Appendix from the center?5. What is the standard equation of the locus of points in the Cartesian plane, the absolutedifference of whose distances from the points (4, 0) is 4?A-TEAM: There is no plan B.Write your complete solution to the following challenger.(5 points) A latus rectum of a central conic is a segment perpendicular to the principal axis 2 2bpassing through a focus. Show that its length is . aSHREK 4EVER AFTER: It ain’t ogre…til it’s ogre.You may get extra points from this portion. (3 bonus points)Write the standard equations of the conics found on the cover page. Points 5,0 , 5,0 , 0,5 , 0, 7 , 0, 7 are foci of the conics.
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