Find the equation of the circle with center at, №18011079, 28.12.2021 03:52

Mathematics

Find the equation of the circle with center at the point (2,3) and a radius of 12 units

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P Answered by Master

✒️CIRCLE EQUATIONS

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$\underline{\mathbb{PROBLEM:}}$

Find the equation of the circle with center at the point (2,3) and a radius of 12 units.

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$\qquad\large\rm» \:\: \green{(x - 2)^2 + (y - 3)^2 = 144}$

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$\underline{\mathbb{SOLUTION:}}$

» The equation of the circle in standard form is written as:

$\rm (x - h)^2 + (y - k)^2 = r^2$

» Where (h,k) is the center and r is the radius. Substitute the given center and the radius to the equation.

$\therefore$ (x - 2)² + (y - 3)² = 144 is the standard form of the equation.

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Mathematics

1. the equation of a circle is x ^2 + y ^2 – 4 x + 2 y = 11 . what are the coordinates of the center of the circle? question 1 options (2, –1) (4, –2) (–4, 2) (–2, 1) 2. what is the equation of the circle with center (4, -3) and radius 2? question 2 options: (x + 4)^2 + (y – 3)^2 = 4 (x + 4)^2 – (y – 3)^4 = 4 (x – 4)^2 + (y + 3)^2 = 2 (x – 4)^2 + (y + 3)^2 = 4 3. what is the equation of this circle? (has picture) (x – 2)^2 + (y – 7)^2 = ½ (x + 2)^2 + (y + 7)^2 = ¼ (x + 7)^2 + (y + 2)^2 = ¼ (x + 2)^2 + (y + 7)^2 = ½ 4. what are the center and radius

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P Answered by PhD

3

Problem 1

x^2 + y^2 - 4x + 2y = 11
x^2 - 4x + y^2 + 2y = 11
(x^2 - 4x) + (y^2 + 2y) = 11
(x^2 - 4x + 4) + (y^2 + 2y) = 11 + 4
(x - 2)^2 + (y^2 + 2y) = 15
(x - 2)^2 + (y^2 + 2y + 1) = 15+1
(x - 2)^2 + (y + 1)^2 = 16

The equation
(x - 2)^2 + (y + 1)^2 = 16
can be written as
(x - 2)^2 + (y - (-1))^2 = 4^2
which is in the form
(x-h)^2 + (y-k)^2 = r^2
where,
center = (h,k) = (2,-1)
radius = r = 4

Choice A) (2,-1)

Problem 2

Given Center = (h,k) = (4,-3)
h = 4, k = -3
Given Radius = r = 2

(x-h)^2 + (y-k)^2 = r^2
(x-4)^2 + (y-(-3))^2 = 2^2
(x-4)^2 + (y+3)^2 = 4

Answer is choice D

Problem 3

Based on the picture, the center is (-2,-7)
(h,k) = (-2,-7)
h = -2
k = -7

Each tick mark is 1/2 a unit. The distance from the red center to the outer edge of the circle is 1 tick or 1/2 a unit. The radius is 1/2 a unit. So r = 1/2 and r^2 = (1/2)^2 = 1/4

(x-h)^2 + (y-k)^2 = r^2
(x-(-2))^2 + (y-(-7))^2 = (1/2)^2
(x+2)^2 + (y+7)^2 = 1/4

Answer is choice B

Problem 4

x^2 + y^2 - 18x + 12y + 68 = 0
(x^2 - 18x) + (y^2 + 12y) + 68 = 0
(x^2 - 18x + 0) + (y^2 + 12y + 0) + 68 = 0
(x^2 - 18x + 81 - 81) + (y^2 + 12y + 36 - 36) + 68 = 0
(x^2 - 18x + 81) - 81 + (y^2 + 12y + 36) - 36 + 68 = 0
(x - 9)^2 + (y + 6)^2 - 81 - 36 + 68 = 0
(x - 9)^2 + (y + 6)^2 - 49 = 0
(x - 9)^2 + (y + 6)^2 = 49
(x - 9)^2 + (y - (-6))^2 = 7^2

The center is (9,-6) and the radius is 7

Problem 5

Center = (h,k) = (-3,7)
Radius = r = 5

(x-h)^2 + (y-k)^2 = r^2
(x-(-3))^2 + (y-7)^2 = 5^2
(x+3)^2 + (y-7)^2 = 25

Answer is choice B

Mathematics

1. the equation of a circle is x ^2 + y ^2 – 4 x + 2 y = 11 . what are the coordinates of the center of the circle? question 1 options (2, –1) (4, –2) (–4, 2) (–2, 1) 2. what is the equation of the circle with center (4, -3) and radius 2? question 2 options: (x + 4)^2 + (y – 3)^2 = 4 (x + 4)^2 – (y – 3)^4 = 4 (x – 4)^2 + (y + 3)^2 = 2 (x – 4)^2 + (y + 3)^2 = 4 3. what is the equation of this circle? (has picture) (x – 2)^2 + (y – 7)^2 = ½ (x + 2)^2 + (y + 7)^2 = ¼ (x + 7)^2 + (y + 2)^2 = ¼ (x + 2)^2 + (y + 7)^2 = ½ 4. what are the center and radius

Step-by-step answer

P Answered by PhD

3

Problem 1

x^2 + y^2 - 4x + 2y = 11
x^2 - 4x + y^2 + 2y = 11
(x^2 - 4x) + (y^2 + 2y) = 11
(x^2 - 4x + 4) + (y^2 + 2y) = 11 + 4
(x - 2)^2 + (y^2 + 2y) = 15
(x - 2)^2 + (y^2 + 2y + 1) = 15+1
(x - 2)^2 + (y + 1)^2 = 16

The equation
(x - 2)^2 + (y + 1)^2 = 16
can be written as
(x - 2)^2 + (y - (-1))^2 = 4^2
which is in the form
(x-h)^2 + (y-k)^2 = r^2
where,
center = (h,k) = (2,-1)
radius = r = 4

Choice A) (2,-1)

Problem 2

Given Center = (h,k) = (4,-3)
h = 4, k = -3
Given Radius = r = 2

(x-h)^2 + (y-k)^2 = r^2
(x-4)^2 + (y-(-3))^2 = 2^2
(x-4)^2 + (y+3)^2 = 4

Answer is choice D

Problem 3

Based on the picture, the center is (-2,-7)
(h,k) = (-2,-7)
h = -2
k = -7

Each tick mark is 1/2 a unit. The distance from the red center to the outer edge of the circle is 1 tick or 1/2 a unit. The radius is 1/2 a unit. So r = 1/2 and r^2 = (1/2)^2 = 1/4

(x-h)^2 + (y-k)^2 = r^2
(x-(-2))^2 + (y-(-7))^2 = (1/2)^2
(x+2)^2 + (y+7)^2 = 1/4

Answer is choice B

Problem 4

x^2 + y^2 - 18x + 12y + 68 = 0
(x^2 - 18x) + (y^2 + 12y) + 68 = 0
(x^2 - 18x + 0) + (y^2 + 12y + 0) + 68 = 0
(x^2 - 18x + 81 - 81) + (y^2 + 12y + 36 - 36) + 68 = 0
(x^2 - 18x + 81) - 81 + (y^2 + 12y + 36) - 36 + 68 = 0
(x - 9)^2 + (y + 6)^2 - 81 - 36 + 68 = 0
(x - 9)^2 + (y + 6)^2 - 49 = 0
(x - 9)^2 + (y + 6)^2 = 49
(x - 9)^2 + (y - (-6))^2 = 7^2

The center is (9,-6) and the radius is 7

Problem 5

Center = (h,k) = (-3,7)
Radius = r = 5

(x-h)^2 + (y-k)^2 = r^2
(x-(-3))^2 + (y-7)^2 = 5^2
(x+3)^2 + (y-7)^2 = 25

Answer is choice B

Mathematics

Item 2 why is circle 1 similar to circle 2? circle 1: center (2, 3) and radius 4 circle 2: center (2, 3) and radius 12 circle 2 is a dilation of circle 1 with a scale factor of 3. circle 1 and circle 2 are reflections of each other. circle 2 is a dilation of circle 1 with a scale factor of 8. circle 1 and circle 2 have the same center.

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P Answered by Specialist

13

Circle 2 is a dilation of circle 1 with a scale factor of 3.

Step-by-step explanation:

Just Because :D

Mathematics

Which transformations can be used to show that circle p is similar to circle q? circle p: center (2, −3) and radius 4 circle q: center (2, 3) and radius 28 select each correct answer! circle p is a dilation of circle q with a scale factor of 24. circle q is a translation of circle p, 6 units up. circle q is a translation of circle p, 6 units left. circle q is a dilation of circle p with a scale factor of 7.

Step-by-step answer

P Answered by Specialist

4

Circle Q is a dilation of circle P with the scale factor of 7
circle Q is a translation of circle P 6 units up

Mathematics

1. a circle has a center at (3,5). the point (3,8) is on the circle. what is the circumference of the to the nearest tenth of a unit? a. 9.4 units b. 18.8 units c. 28.3 units d. 56.5 units 2. a triangle has a perimeter of exactly 24 units. which of the following could be the vertices of the triangle? a. (-1 ,3 ), (2,-1), (-1,-1) b. (6,0), (6,7), (0,7) c. (-1,-1), (-6,-13), (-9,-9) ,-4) (-3,4), (3,4) 3. a circle has an area of approximately 78.5 square units. if the center of the circle is at (2,4). which of the following points is on the circle?

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P Answered by PhD

20

1. B
Radius of circle = 3 units
C = 2πr
C = 18.8 units

2. D
The distances between the points add to 24.

3. B
A = πr²
r = √(78.5/π)
r = 5 units
Point from options that is 5 units from (2,4) is (2,-1)

4. A
length of diameter = √[(5 - 1)² + (5 - 2)]
d = 5
r = 5/2

A = πr²
A = 25/4 pi units²

Mathematics

Write the standard equation for the circle. center (-6 9) r=3 a. (x-9)^2+(y+6)^2=9 b. (x+6)^2+(y-9)^2=3 c. (x-6)^2+(y+9)^2=3 d. (x+6)^2+(y-9)^2=9 find the center and radius of the circle with equation (x+2)^2+(y+10)2=4 a. center (-2, -10); r=2 b. center (2, 10); r=4 c. center (-2, -10); r=4 d. center (10, 2); r=2 what is the equation of the fircle with center 3,5 that passes through the point (-4, 10)? a. (x-3)^2 + (y-5)^2 = 226 b. (x+4)^2 + (y-10)^2 = 74 c. (x+4)^2 + (y-10)^2 = 226 d. (x+3)^2 + (y-5)^2 = 74 what is the equation of the circle with

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P Answered by PhD

6

The equation of the circle with center (h, k) and radius r is
.. (x -h)^2 +(y -k)^2 = r^2

1. selection D matches the specification of the circle

2. selection A matches the given equation

3. None of the offered selections matches
.. (x -3)^2 +(y -5)^2 = 74

4. selection A matches the requirements
Write the standard equation for the circle. center (-6 9) r=3 a. (x-9)^2+(y+6)^2=9 b. (x+6)^2+(y-9)

Write the standard equation for the circle. center (-6 9) r=3 a. (x-9)^2+(y+6)^2=9 b. (x+6)^2+(y-9)

Mathematics

Which transformations can be used to show that circle p is similar to circle q? circle p: center (2, −3) and radius 4 circle q: center (2, 3) and radius 28 select each correct answer. circle q is a dilation of circle p with a scale factor of 7. circle q is a translation of circle p, 6 units up. circle q is a translation of circle p, 6 units left. circle p is a dilation of circle q with a scale factor of 24.

Step-by-step answer

P Answered by Specialist

58

The Selected correct answers are.

Circle Q is a dilation of circle P with a scale factor of 7.

Circle Q is a translation of circle P, 6 units up.

Mathematics

Write the standard equation for the circle. center (-6 9) r=3 a. (x-9)^2+(y+6)^2=9 b. (x+6)^2+(y-9)^2=3 c. (x-6)^2+(y+9)^2=3 d. (x+6)^2+(y-9)^2=9 find the center and radius of the circle with equation (x+2)^2+(y+10)2=4 a. center (-2, -10); r=2 b. center (2, 10); r=4 c. center (-2, -10); r=4 d. center (10, 2); r=2 what is the equation of the fircle with center 3,5 that passes through the point (-4, 10)? a. (x-3)^2 + (y-5)^2 = 226 b. (x+4)^2 + (y-10)^2 = 74 c. (x+4)^2 + (y-10)^2 = 226 d. (x+3)^2 + (y-5)^2 = 74 what is the equation of the circle with

Step-by-step answer

P Answered by PhD

6

The equation of the circle with center (h, k) and radius r is
.. (x -h)^2 +(y -k)^2 = r^2

1. selection D matches the specification of the circle

2. selection A matches the given equation

3. None of the offered selections matches
.. (x -3)^2 +(y -5)^2 = 74

4. selection A matches the requirements
Write the standard equation for the circle. center (-6 9) r=3 a. (x-9)^2+(y+6)^2=9 b. (x+6)^2+(y-9)

Mathematics

Which transformations can be used to show that circle p is similar to circle q? circle p: center (2, −3) and radius 4 circle q: center (2, 3) and radius 28 select each correct answer. circle q is a dilation of circle p with a scale factor of 7. circle q is a translation of circle p, 6 units up. circle q is a translation of circle p, 6 units left. circle p is a dilation of circle q with a scale factor of 24.

Step-by-step answer

P Answered by Specialist

58

The Selected correct answers are.

Circle Q is a dilation of circle P with a scale factor of 7.

Circle Q is a translation of circle P, 6 units up.

Find the equation of the circle with center at the point (2,3) and a radius of 12 units

Step-by-step answer

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