Name: ___________________________________________________
Mrs. White
Unit 13 Homework Packet
Day 1 Homework
Determine the Center and Radius of the given circles.
1. (𝑥 − 7)2 + (𝑦 + 10)2 = 81
4. 36 = (𝑥 + 8)2 + (𝑦 + 7)2
2. 100 = (𝑥 + 3)2 + 𝑦 2
5. 0 = (𝑥 − 1)2 + (𝑦 − 11)2 − 9
3. (𝑥 − 9)2 + (𝑦 + 2)2 = 1
Graph the following circles.
6. (𝑥 − 3)2 + (𝑦 + 2)2 = 4
7. 𝑥 2 + (𝑦 − 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. (𝑥 − 7)2 + (𝑦 + 10)2 = 81
2. 100 = (𝑥 + 3)2 + 𝑦 2
Determine the Center and Radius of the given circles by completing the square.
3. 𝑥 2 + 𝑦 2 − 4𝑥 + 14𝑦 + 17 = 0
Center (_______,_______)
Radius = ____________
4. 𝑥 2 + 𝑦 2 + 4𝑥 − 16𝑦 + 52 = 0
Center (_______,_______)
Radius = ____________
5. 𝑥 2 − 14𝑥 + 𝑦 2 − 2𝑦 − 50 = 0
Center (_______,_______)
Radius = ____________
6. 𝑥 2 + 2𝑥 − 18 = −𝑦 2 + 8𝑥
Center (_______,_______)
Radius = ____________
Day 3 Homework
Determine the Center and Radius of the given circles.
1. (𝑥 − 5)2 + (𝑦 + 8)2 = 16
Center (_______,_______)
Radius = ____________
2. 25 = 𝑥 2 + (𝑦 − 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. (𝑥 − 7)2 + (𝑦 + 10)2 = 81
Determine the Center and Radius of the given circles by completing the square.
9. 𝑥 2 + 𝑦 2 + 14𝑥 − 12𝑦 + 4 = 0
Center (_______,_______)
Radius = ____________
10. 𝑥 2 + 2𝑥 + 𝑦 2 = 55 + 10𝑦
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 𝜋 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 𝜋 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 𝜋 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 𝜋 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 ̅̅̅̅̅̅
𝐴𝑂𝐵 is drawn,
̅̅̅̅ is drawn to the circle at
tangent 𝐶𝐵
B, E is a point on the circle and ̅̅̅̅
𝐵𝐸 ∥
̅̅̅̅̅̅̅
𝐴𝐷𝐶 . Prove that ∆𝐴𝐵𝐸~∆𝐶𝐴𝐵