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ANALYSIS

SCORE: DATE: 28 June 2011 NAME: CLASS TIME CLASS ID: M5 1PS1 – Conics

FOUR SECTIONS, ONE DESTINY

ECLIPSE: (5 points) TOY STORY: (10 points)

1. 1. 6.

2. 2. 7.

3. 3. 8.

4. 4. 9.

5. 5. 10.

KILLERS: (10 points) KARATE KID: (15 points)

1. 1.

2. 2.

3. 3.

4. 4.

5. 5.

A-TEAM: (5 points) SHREK: (3 points)

PARABOLA

ELLIPSE

HYPERBOLA

Math 5 Problem Set 1 SY 2011-2012

Conics

INSTRUCTIONS:

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.

Non-compliance with the instructions will automatically mean a grade of zero.

x

y

M5 1PS1

ECLIPSE : It all begins…with a choice. Write the CAPITAL LETTER that corresponds to the correct answer. (1 pt each)

1. Which of the corresponding parts of an ellipse is farthest from its center?

M. directrix A. extremity T. latus rectum H. vertex 2. A satellite dish is in the form of a paraboloid ( a 3D figure formed by rotating a parabola about its axis). Its receiver is located at the focus which is 25cm from the vertex of the paraboloid. If the dish is 9cm deep at the center, what is the area of its circular rim?

M. 900 sq.cm. A. 225 sq.cm. T. 60 sq.cm. H. 25 sq.cm. 3. If an ellipse and a parabola share a focus and corresponding vertex, which of these is true?

M. The parabola has a shorter latus rectum. T. The length of LR of the conics are equal. A. The ellipse has a shorter latus rectum. H. The lengths of LR cannot be compared.

4. The lines 512

y x are asymptotes of a hyperbola whose foci are 26 units apart. Which

CANNOT be a vertex of the hyperbola?

M. (– 12, 0) A. (0, 5) T. (0, – 12) H. (12, 0)

5. What type of hyperbola is 2 29x 16y 54x 32y 209 0 ?

M. degenerate A. equilateral T. horizontal H. vertical TOY STORY: No toy gets left behind. 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 parallel to exactly two generators of the cone.

2. Identify the set of points in a plane the sum of whose distances from two fixed points is a constant.

3. The graph of 2y y 2 0 is a degenerate form of what conic?

4. What is the orientation of the ellipse whose major axis is vertical? 5. Locate the coordinates of the intersection of the asymptotes of the hyperbola

2 2

1 2 1 y x ?

6. What is the length of the transverse axis of an equilateral hyperbola whose conjugate axis has

endpoints at (– 1, 5) and (– 1, –1)?

7. If the quotient of the eccentricities of a hyperbola and a parabola is 2/3, what is the product?

8. What is the length of the conjugate axis of the hyperbola

2 2

125 144

y x

?

9. What is the distance between the focus and the directrix of a parabola whose latus rectum is 2 units long?

10. Find an equation of the principal axis of the conic

2 2

3 41

9 16

x y.

KILLERS: …give it your best shot. Write the most appropriate answer in simplest form. (2 pts each; no partial points)

1. An ellipse with eccentricity 12

has major axis of length 2. How long is its minor axis?

2. What is the general equation of the asymptote with a positive slope of the hyperbola

2 2x y 2x 2y 1 0 ?

3. If the distance between an endpoint of the latus rectum to the vertex of a parabola is 80, then what is the length of the latus rectum?

4. What is the graph of 2 2x y 2x 6y 14 0 ?

5. What is the standard equation of the ellipse with center at (2, – 1), focus at (– 3, – 1) and 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 are the coordinates of the vertex closest to the given focus?

2. A ball is thrown from the ground and moves along a parabolic path 2

s(t) 16t 32t

where s(t) meters is the vertical displacement in t seconds. At what time, in seconds, will the ball reach 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? 4. A semi-elliptical tunnel is 10 feet across and 4 feet high. How high is the ceiling 3 feet from the center? 5. What is the standard equation of the locus of points in the Cartesian plane, the absolute

difference 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

passing through a focus. Show that its length is

22b

a.

SHREK 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.

The coverage of the first long test on the last meeting next week is CONIC SECTIONS.

TCWAG6: Chapter 10 OR TC7: Appendix