What is the general equation of a circle centered at the point (h, k)

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There are free response questions that must show work on the free response....but for the multiple choice the correct answer is suffucient

1. What is the general equation of a circle centered at the point (h, k)? 3 points QUESTION 2 1. What is the equation of the circle with center at (2, 4) and radius of 6? 3 points QUESTION 3 1. What is the general equation of a circle centered at the origin? 3 points QUESTION 4 1. Find the equation of the circle with center at (3, 2) and through the point (5, 4). 3 points QUESTION 5 1. If a circle has a center at the point (3, 4) and goes through the point (6, 8), what is the radius? 3 points QUESTION 6 1. Find the equation of the circle with center at (-3, 1) and through the point (2, 13). 3 points QUESTION 7 1. What is the center and radius of the following circle: x2 + (y – 6)2 = 50 3 points QUESTION 8 1. What is the diameter of the following circle: (x + 4)2 + (y – 9)2 = 18 3 points QUESTION 9 1. What is the equation of the circle with center at (-3, 0) and diameter 20? 3 points QUESTION 10-8.03 WRITING THE EQUATIONS OF A CIRC SHORT ANSWER 1. What is the center and radius of the following circle: (x – 5)2 + (y + 2)2 = 16 1. is the hypotenuse of the right triangle below. True False 2 points 1. QUESTION 2 Identify the leg(s) of the right triangle below. and and and 2 points 1. QUESTION 3 Identify the legs in the right triangle below. 3 points 1. QUESTION 4 You help your dad build a dog house for your dog. You tell him that it would be easy to build a dog house in the shape of a tent. The slanted sides are 5 feet long and the bottom of the house is 6 feet across. You draw him the following illustration to help him find the height of the dog house. What do you tell him the height of the dog house is? 9 ft 4 ft 16 ft 4.5 ft 2 points QUESTION 5 1. A suitcase measures 36 inches long and 24 inches high. What is the diagonal length of the suitcase? 43.2 in 32.3 in 12.8 in 29.3 in 2 points QUESTION 6 1. Find the length of 3 points 1. QUESTION 7 In the triangle below, what ratio is sin θ? 2 points 1. QUESTION 8 In the triangle below, determine the value of c. 2.5 11.5 9.6 2.3 2 points QUESTION 9 1. In the triangle below, determine the measure of side a. 3 points 1. QUESTION 10 In the triangle below, what ratio is cos P? 2 points QUESTION 11 1. In the triangle below, determine the value of c. 37.3 34.1 54.7 74.8 2 points 1. QUESTION 12 In the triangle below, what ratio is cos θ? 3 points QUESTION 13 1. In the triangle below, determine the value of c. 2.5 1 1.9 2.3 2 points 1. QUESTION 14 In the triangle below, what ratio is tan θ? 2 points 1. QUESTION 15 In the triangle below, determine the value of a. 3 points QUESTION 16 1. In the triangle below, the csc X is True False 2 points 1. QUESTION 17 In the triangle below, what ratio represents csc Y? 2 points 1. QUESTION 18 In the triangle below, what ratio represents csc θ? 3 points 1. QUESTION 19 In the triangle below, what ratio represents sec Y? 2 points QUESTION 20 1. Secant is the reciprocal of which other ratio? Sine Cosine Cotangent Cosecant 2 points QUESTION 21 1. Complete the statement: Cosine is the reciprocal of the ___________ ratio. 3 points QUESTION 22 1. In the triangle below, what ratio represents cot θ? 2 points QUESTION 23 1. In the triangle below, the cot θ is True False 2 points QUESTION 24 1. Complete the statement: Cosecant is the reciprocal of the ___________ ratio 3 points 1. QUESTION 25 Your parents surprise you with a hot air balloon ride above the city. From a hot air balloon, the angle between a radio antenna straight below and the base of your house is 70°, as shown below. If the height of the balloon is 5 miles, what is the distance between the radio antenna and your house? 23.1 miles 4.69 miles 1.7 miles 13.7 miles 2 points QUESTION 26 1. If the height of the building is 100 feet and the sun makes a 50 degree angle with the ground as shown in the image below, what is the distance from the top of the building to the tip of the shadow? 75.4 feet 130.5 feet 76.6 feet 331.3 feet 2 points QUESTION 27 1. The angle of elevation of a ladder leaning against a wall is 45°. If the distance from the base of the ladder to the wall is 12 feet, how long is the ladder? 8.49 feet 16.97 feet 15.87 feet 29.8 feet 2 points QUESTION 28 1. The length of the one side of a square is 24 cm. Find the length of the diagonal. 3 points QUESTION 29 1. What is the y-value of sin(x) when x = 180°? 0 -1 2 points QUESTION 30 1. Which of the following graphs is f(x) = sin(x)? 2 points QUESTION 31 1. What is the y-value of sin(x) when x= -360°? 3 points QUESTION 32 1. For what x-value(s) does cos(x) = 1? -360° 0° 360° all of the above 2 points QUESTION 33 1. What is the domain and range of f(x) = cos(x)? The domain is all real numbers and the range is The domain is and the range is all real numbers. The domain is all real numbers and the range is The domain is all real numbers and the range is 2 points QUESTION 34 1. For what x-value(s) does cos(x) = 0? 3 points QUESTION 35 1. The following is the graph of f(x) = tan(x). True False 2 points QUESTION 36 1. The y-value of tan(x) when x = -90° and x = 90° is undefined. True False 2 points QUESTION 37 1. What is the y-value for f(x) = tan(x) when x = -45°? 3 points QUESTION 38 1. Find the 65.5° 99.9° 65.4° 35.4° 2 points 1. QUESTION 39 Write an equation that could be used to find the value of y. 2 points QUESTION 40 1. Find the 3 points 1. QUESTION 41 Write an equation that could be used to find the value of b. 382 = 22 + 32 – 2(2)(3)(cos b°) b2 = 22 + 32 – 2(2)(3)(cos 38°) 22 = b2 + 32 – 2(b)(3)(cos 38°) 32 = 22 + b2 – 2(2)(b)(cos 38°) 2 points QUESTION 42 1. Write an equation that could be used to find the 162 = 142 + 102 – 2(5)(6)(cos R) 102 = 142 + 162 – 2(14)(16)(cos R) 142 = 162 + 102 – 2(16)(10)(cos R) 162 = 142 + 102 – 2(14)(10)(cos R) 2 points QUESTION 43-9.05 RIGHT TRIANGLE AND TRIG UNIT 1. Find 3 points

Tutor Answer

Aljon2017
School: Purdue University

Hi, please see attached file for the solution.Please check if I got everything covered.

QUESTION 1

What is the general equation of a circle centered at the point (h, k)?
The general equation of a circle with center at (h, k) and radius r can be computed by first determining its
center-radius form which is:
(x - h)2 + (y - k)2 = r2
x2 – 2hx +h2 +y2 – 2ky + k2 = r2
x2 + y2 – 2hx – 2ky +(h2 + k2 - r2) = 0
ANSWER
3 points

QUESTION 2
What is the equation of the circle with center at (2, 4) and radius of 6?
h=2
k=4
r=6
(x – 2)2 + (y – 4)2 = 62
x2 – 4x + 4 + y2 – 8y + 16 = 36
x2 – 4x + y2 – 8y –16 = 0
ANSWER
3 points

QUESTION 3

What is the general equation of a circle centered at the origin?
h=0
k=0
r=r
(x - 0)2 + (y – 0)2 = r2
x2 + y2 – r2 = 0
ANSWER

3 points

QUESTION 4

Find the equation of the circle with center at (3, 2) and through the point (5, 4).
The radius can be computed using the distance formula:
r = √(𝑦2 − 𝑦1 )2 + (𝑥2 − 𝑥1 )2 = √(4 − 2)2 + (5 − 3)2 = 2√2
h=3
k=2
x2 + y2 – 2hx – 2ky +(h2 + k2 - r2) = 0
x2 + y2 – 2(3) x – 2(2)y +(32 + 22 – (2√2)2) = 0
x2 + y2 – 6x – 4y + 21 = 0
ANSWER

3 points

QUESTION 5

If a circle has a center at the point (3, 4) and goes through the point (6, 8), what is the radius?
The radius can be computed using the distance formula:
r = √(𝑦2 − 𝑦1 )2 + (𝑥2 − 𝑥1 )2 = √(8 − 4)2 + (6 − 3)2 = 5

ANSWER

3 points

QUESTION 6

Find the equation of the circle with center at (-3, 1) and through the point (2, 13).
The radius can be computed using the distance formula:
r = √(𝑦2 − 𝑦1 )2 + (𝑥2 − 𝑥1 )2 = √(13 − 1)2 + (2 − (−3))2 = 13
h=-3
k=1
x...

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Anonymous
Excellent job

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