Math12a Circle Geometry Multiple Choice

MATH12A CIRCLE GEOMETRY MULTIPLE CHOICE

1. An image of the unit circle is produced by the mapping rule (x, y)  (3x  2,3y  4). What is the diameter of the new circle?

(a) 3 (b) 3 (c) 6 (d) 9

2. John uses the process of completing the square to determine the center of the circle 2x 2  2y 2 16x  32y  34 but makes an error. Which step contains the key critical error?

(a) step 1 2(x 2  8x)  2(y 2 16y)  34 (b) step 2 2(x 2  8x 16)  2(y 2 16y  64)  34 16  64 (c) step 3 2(x  4)2  2(y  8) 2  114 (d) step 4 (x  4) 2  (y  8)2  57

3. Which of the following equations represents an ellipse with major axis on the x-axis and having a length of 12 units?

x 2 y 2 x 2 y 2 (a)   1 (b)   1 6 36 36 64 x 2 y 2 x 2 y 2 (c)   1 (d)   1 36 36 36 9

4. Which point below lies on the circle with equation (x  3) 2  (y  3) 2  90:

(a) (3,3) (b) (2,3) (c) (1,3) (d) (0,3)

5. Given the following diagram, what is the measure of the angle ?

(a) 40 40° (b) 15 c θ (c) 20

(d) 30 6. Given that AB has a midpoint of M (2,3) and endpoint B(5,1) what are the coordinates of A?

(a) (1,4) (b) (1.5,1) (c) (9,7) (d)(3.5,2)

7. Given the following diagram of rectangle ABCD, what is the slope of side CD ? A

1 D (a)  (b) -3 B(4,6) 3 1 (c) 3 (d) C(2,0) 3

8. Given the following diagram, where C is the center of the circle, how far away from the center of the circle is chord AB, if the radius of the circle is 10cm?

(a) 7.1 cm

(b) 6.6 cm C (c) 9.7 cm ˙ 14 cm (d) 4.9 cm A B

9. What is the equation of the given circle? (C is the center of the circle)

(a) (x 1) 2  (y  3) 2  100 (x 1) 2  (y  3) 2  100 (b) (-2,-1) C (4,7) (c) (x 1) 2  (y  3) 2  25 (d) (x 1) 2  (y  3) 2  25

10. Which of the following statements would always be true for two chords in the same circle that are equal in length?

(a) They are parallel (b) They are perpendicular (c) They are the same distance from the center of the circle (d) They are the same length as the diameter of the circle MATH 12A TEST CIRCLE GEOMETRY

MATHEMATICIAN______

PART 1: SELECTED RESPONSE (VALUE: 10 POINTS) Place your answers here!

1.______6.______

2.______7.______

3.______8.______

4.______9.______

5.______10.______

PART 2: CONSTRUCTED RESPONSE (VALUE: POINTS) Read each question carefully and write your response in the space provided. Show all of your work, as points will be given for correct method as well as for a correct answer. When using decimals, all answers must be rounded off to the nearest hundredth .

1. Write the converse of each statement. Where possible also give the “iff” statement. (1 point each)

(a) If it is raining, then the grass must be wet.

(b) If a quadrilateral is a square, then it has four right angles.

(c) If two chords of a circle are congruent, then they are equidistant from the center of the circle. 2. Solve for the missing angles and include a reasons for each answer:

(a) Answers Reasons

24 1  40 45 2  2 3 1 4 3 

4 

5 5  (b) C B C  32 , AED  60 and mAB  66 A F D

Answers Reasons

ADB 

BAD 

BAE 

BDE 

mAE 

mED 

3. Given that PS  RS and SQ is the bisector ofPSR, prove that PQR is isosceles.

Statements Reasons

4. Given AOB is equilateral with AB = 9cm. AOB is a central angle. a) What is the perimeter of the shaded region? b) What is the area of the shaded region?

2 2 1  1  5. Use the circle (x  6)  (y  4)  1 to answer the following questions: 8  8 

(a) State the center of the circle ______(b) State the radius of the circle ______

(c) Write a mapping rule that would transform the unit circle onto this circle

______

(d) Does the point P(-1,0) lie on, outside, or inside the circle?

______

(e) Write the equation of a new circle in transformational form that has the same radius, but is moved 3 units to the left and 2 units up.

______

6. In an ellipse A(-7,2) and B(3,2) are the endpoints of the major axis, and C(-2,-1) and D(-2,5) are the endpoints of the minor axis. Draw a sketch, then determine the equation of the ellipse in general form.

7. Given the ellipse whose equation is 4x 2  9y 2  48x  72y 144  0, complete each of the following:

(a) Write the equation in standard form (b) Write the equation in transformational form

(c) State the: (d) Graph

Center ______

Major Axis ______

Minor Axis ______

Formulas

General: Standard: Transformational: or