Name: ___________________________________________________ Mrs. White Unit 13 Homework Packet Day 1 Homework Determine the Center and Radius of the given circles. 1. ( − 7)2 + ( + 10)2 = 81 4. 36 = ( + 8)2 + ( + 7)2 2. 100 = ( + 3)2 + 2 5. 0 = ( − 1)2 + ( − 11)2 − 9 3. ( − 9)2 + ( + 2)2 = 1 Graph the following circles. 6. ( − 3)2 + ( + 2)2 = 4 7. 2 + ( − 5)2 = 25 8. Write the equation of the circle with a center at (2, 0) and passing through the point (8, 8). 9. Write the equation for the circles described below. a. diameter = 12, center at (-3, 2) b. radius = 7, center at (9, 3) c. radius = d. diameter = 11, center at (0, 5) 17 , center at (-1, -1) 10. The circle in the diagram has a radius length of 6 and is tangent to both the x-axis and the y-axis. Write the equation of this circle. 11. Write the equation of the circle whose diameter has endpoints of (-2, 2) and (0, 4). Day 2 Homework Put each circle in general form. 1. ( − 7)2 + ( + 10)2 = 81 2. 100 = ( + 3)2 + 2 Determine the Center and Radius of the given circles by completing the square. 3. 2 + 2 − 4 + 14 + 17 = 0 Center (_______,_______) Radius = ____________ 4. 2 + 2 + 4 − 16 + 52 = 0 Center (_______,_______) Radius = ____________ 5. 2 − 14 + 2 − 2 − 50 = 0 Center (_______,_______) Radius = ____________ 6. 2 + 2 − 18 = − 2 + 8 Center (_______,_______) Radius = ____________ Day 3 Homework Determine the Center and Radius of the given circles. 1. ( − 5)2 + ( + 8)2 = 16 Center (_______,_______) Radius = ____________ 2. 25 = 2 + ( − 7)2 Center (_______,_______) Radius = ____________ Determine the equation of circle C. 3. Radius = 8cm, C(2,-6) _________________________________________ 4. 7. Radius = √7 cm, C(-3, -1) _________________________________________ 5. Graph the following circle. x2 + y2 + 8x + 4y + 11 = 0 Write the standard form of a circle based on the given information. 6. Center: (2, -5), Point on Circle: (-7, -1) Write the standard form of a circle based on the given information. 7. Endpoints of diameter: (-3, 11) and (3, -13) 8. Put each circle in general form. ( − 7)2 + ( + 10)2 = 81 Determine the Center and Radius of the given circles by completing the square. 9. 2 + 2 + 14 − 12 + 4 = 0 Center (_______,_______) Radius = ____________ 10. 2 + 2 + 2 = 55 + 10 Center (_______,_______) Radius = ____________ 11. The circle shown in the diagram has a center at (-3, 4) and passes through the origin. Write an equation of this circle. Day 4 Homework 1. Your dog, Rex, is attached to a 4 foot leash that is tied to a stake. He moves away from the stake so that the leash is extended completely. From there, he runs around in a circle, but he only travels 178° of the circle. How far, to the nearest foot, did he travel? 5. The beam from a lighthouse is visible for a distance of 3 miles. To the nearest square mile, what is the area covered by the beam as it sweeps on arc of 150o? Day 5 Homework Convert the following to radians. 1. 30 2. -45 4. - 135 5. 85 3. 180 Convert the following radians to degrees. 6. 5 3 7. 7 4 9. 2 5 10. 4.2 8. 9 6 11. Jake says “Two circles are always similar no matter what because you can map one onto the other using similarity transformations!!” What transformations might he be referring to? 12. Two circles A and B have different radii. A student dilates circle A at its center by a scale factor of 9 to make it the same size as circle B. What scale factor could have been used to 4 make circle B the same size as circle A? 13. Circle A and circle B are concentric. a) What does that mean? b) If the radius of circle A is 24 cm and the radius of circle B is 18 cm. What scale factor would map circle A onto circle B? 14. Determine the sequence of transformations that would map circle A onto circle B. a) b) A A B B 15. How many radians are in one circle? 16. How many radians are in 3 circles? 17. a) What is the formula for the area of a sector? b) How does this formula change if you are given an angle in radian measure instead of degrees? 18. a) What is the formula for the length of an arc of a circle? b) How does this formula change if you are given an angle in radian measure instead of degrees? Day 6 Homework 1. Find the arc length shown in the diagram to the right. Give your answers in terms of pi and rounded to the nearest hundredth. 2. Find the area of the unshaded sector to the nearest hundredth. 3. Determine the translation vector that would map the center of circle A onto the center of circle B. a) b) Circle A A (-4, 5) Circle B B (3, 0) c) Circle A 1 4 A ,7 Circle B 3 4 Circle A A (0, -8) B 3 , 2 Circle B B (-3, 2) 4. What scale factor would make circle A the same size as circle B? a) b) Circle A RadiusA = 2cm Circle B RadiusB = 4cm Scale Factor: _____ c) Circle A RadiusA = 7cm Circle B RadiusB = 6 cm Scale Factor: _____ Circle A RadiusA = 6cm Circle B RadiusB = 8cm Scale Factor: _____ 5. Name the series of transformations that would map circle A onto circle B. B A 6. Harrison has a circular patio in his back yard. The patio has a radius of 7 feet. He has mapped out a section along the edge of the circle to put bricks on. If the radii connecting the 5 4 center of the patio to the edges of the arc forms an angle that is radians, find the length of the arc, to the nearest tenth of a foot. 6 7. A sector of a circle with a 3 in radius forms a central angle of 7 radians. What is the area of this sector? 8. Find the center and radius of the circle with the following equation: x2 + 10x + y2 - 4y= -22 9. Write the equation of a circle that has a diameter with the endpoints (5, 4) and (-3, 2). 10. Convert 45° to radians. 9 11. Convert 5 to degrees. Day 7 Homework 1. Circle O, is a diameter with and chords and Prove: 2. intersect at E. parallel to chord , chords and are drawn, 3. 4. 3 5. A sector of a circle with a 9 in radius forms a central angle of 2 radians. What is the area of the rest of the circle? Day 8 Homework 1. 2. Given the diagram below with chords as shown, Prove: AD AE BD BC 3. 4. In the accompanying diagram of circle O, diameter ̅̅̅̅̅̅ is drawn, ̅̅̅̅ is drawn to the circle at tangent B, E is a point on the circle and ̅̅̅̅ ∥ ̅̅̅̅̅̅̅ . Prove that ∆~∆

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# Name: Mrs. White Unit 13 Homework Packet Day 1 Homework