What are the center and the radius of the circle 4x2 + 4y2 - 4x + 16y + 1 = 0?

Answers

Answer 1

Answer:

Center of circle: (1, -2)

Radius: √6

Step-by-step explanation:

First, we need to isolate the constant:

Then, we can divide the whole equation by 4:

Then, we can complete the square(reminder: (a+b)^2 = a^2 + 2ab + b^2)

Now that we got the standard equation of the circle, we can find the center and radius by using the equation , where (h, k) is the coordinate of the center, and r is the radius.

Therefore, the center of the circle is (1, -2), and the radius of the circle is √6.

Step-by-step explanation:

Answer 2

The center and radius of the circle 4x² + 4y² - 4x + 16y + 1 = 0 are (1/2, -2) and  2 respectively.

To solve the question, we need to know the standard equation of a circle.

What is the standard equation of a circle?

The standard equation of a circle with center (h,k) and radius, r is

(x - h)² + (y - k)² = r²  (1)

Now, to find the center and radius of 4x² + 4y² - 4x + 16y + 1 = 0, we convert it to standard form by completing the square method.

What is completing the square method?

This is a mathematical operation in which we convert a mathematical expression into a perfect square.

So, 4x² + 4y² - 4x + 16y + 1 = 0

Subtracting 1 from both sides, we have

4x² + 4y² - 4x + 16y + 1 - 1 = 0 - 1

4x² + 4y² - 4x + 16y = - 1

Divding through by 4, we have

x² + y² - x + 4y = -1/4

Adding half the square of the coefficient of x and y to both sides, we have

x² + y² - x + 4y + (-1/2)² + 2² = -1/4 + (-1/2)² + 2²

x² - x + (-1/2)² + y² + 4y + 2² = -1/4 + 1/4 + 2²

(x - 1/2)² + (y + 2)² = 0 + 2²

(x - 1/2)² + (y + 2)² = 2²  (2)

Comparing equations (1) and (2), we have h = 1/2, k = -2 and r = 2.

So, the center and radius of the circle 4x² + 4y² - 4x + 16y + 1 = 0 are (1/2, -2) and  2 respectively.

Learn more about standard equation of a circle here:

brainly.com/question/7622620


Related Questions

Someone plz help me giving brainliest!

Answers

Answer:

the estimate is : 39 7/32

the answer is :   46  9/35

PLEASE HELP I"LL MARK YOU THE BRAINLEST AND GIVE YOU ADDITIONAL POINTS> HELP ITS DUE VERY SOON. To answer this question you must divide the shape into two triangles and a rectangle and add the sums of the areas together.

You work as a custodian at a school and are responsible for wiping cafeteria tables in the shape shown. Each spray bottle covers 200 square feet, and you need to clean 6 tables.

If you have 4 bottles of spray, do you have enough to clean all 6 tables?
Yes, because the area of all 6 tables is 420 sq. ft., and the spray covers 800 sq. ft.
Yes, because the area of all 6 tables is 432 sq. ft., and the spray covers 800 sq. ft.
Yes, because the area of all 6 tables is 768 sq. ft., and the spray covers 800 sq. ft.
No, because the area of all 6 tables is 804 sq. ft., and the spray only covers 800 sq. ft.
No, because the area of all 6 tables is 912 sq. ft., and the spray only covers 800 sq. ft.

Answers

Answer:

option E

Step-by-step explanation:

No, because the area of all 6 table is 912 sq .ft

and the spray only covers 800 sq .ft .

plz mark my answer as brainlist plzzzz.

hope this will be helpful to you .

No, because the area of all 6 tables is 912 sq ft and the spray only covers 800 sq feet. To find the area of the the table, we have to account for the two ends of the tables shaped like triangles. So this means we will find the area of those by doing 2(b•h•1/2)

8•3= 24
24• 1/2= 12
This means 12 is the area of one triangle, but we have two of those so...

12+12=24

Now to find the area of the rectangle we do (b•h)
16•8= 128

Add it all together and...
128+ 24= 152

We have 6 tables in total so multiply it by 6
152• 6= 912

We have 6 tables so...
156•6= 912 sq

There we go. We need 912 sq, and we only have enough to cover 800 sq. So no.

(18x 5 + 6x 4 - 12x 3) ÷ 6x 2

Answers

your answer would be 26.
if u want reasoning just ask!
If I am reading this correctly but I might not because those could be x’s not times. If you follow PEMDAS(please excuse my dear aunt sally helps you remember) you start with parentheses then move to exponents then do you multiplication and Divison and addition and subtraction. So (18 x 5 + 6 x 4 - 12 x 3) you start there 18 x 5 is 90, 6 x 4 is 24, 12 x 3 is 36 so then add 90 +24 which is 114 and then minus 36 from 114. Which is 78. After all that go to 6 x 2 which is 12 from there you would have 78 divided by 12 which equals 6.5. Hopefully that helps but since I could tell if the they were x’s or times.

anyone help with this?

Answers

its answer choice a

Amy needs to order a shade for a triangular-shaped window that has a base of 6 feet and a height of 8 feet. What is the area of the shade?


The area of the shade is
ft2.
Amy needs to order a shade for a triangular-shaped window that has a base of 6 feet and a height of 8 feet. What is the area of the shade?


The area of the shade is
ft2.

Answers

Answer:

24ft.

Step-by-step explanation:

Formula: (LxW)/2

6x8=48

48/2=24

answer; 24

The length of a rectangle is 3 times the width. If
the length is decreased by 4m and the width is
increased by 1m, the perimeter will be 66m.
Determine the dimensions of the original rectangle.

Answers

Answer:

Length = 27 metresWidth = 9 meters

Step-by-step explanation:

I’m not sure but yes

Find the perimeter of this semi-circle with diameter 62cm.
Give your answer as an expression in terms of Pi

Please include the formula

Answers

Step-by-step explanation:

hope it helps

have a great day!!

State whether the indicated angle pairs are adjacent or not. An explanation would be nice, but you don't have to.

Answers

1. Yes, angles a and b have a common vertex (starting point) and a common side (the line between angle a and b). They do not overlap.

2. No, angles a and b share a common vertex but not a common side.

3. No. Same as above.

4. Yes, anlges a and b share a common vertex and side.

Find the measure of < 3 in the figure if the measure of < 2 is 130

Answers

Answer:

50

Step-by-step explanation:

All angles around a circle is 360°

/_ 2 = 130°

/_ 1 = 130° (Vertically opposite angles)

= 130° + 130° = 260°

all angles = 360°

= 360° - 260° = 100°

= 100° ÷ 2

= 50°

= /_ 3 and /_ 4 = 50°

Verification = 130° + 130° + 50° + 50° = 360°

The table shows the balance of two accounts each year for four years. Determine whether each balance is linear or nonlinear. Then predict which account will have a greater balance in Year 3.

Year, t Account A Balance Account B Balance
0 $450 $550
1 $504 $570
2 $564.48 $590

Account A Balance is linear. Account B Balance is nonlinear. Account A will have a greater balance in Year 3.

Account A Balance is nonlinear. Account B Balance is linear. Account A will have a greater balance in Year 3.

Account A Balance is linear. Account B Balance is nonlinear. Account B will have a greater balance in Year 3.

Account A Balance is nonlinear. Account B Balance is linear. Account B will have a greater balance in Year 3.

Answers

Account A Balance is nonlinear. Account B Balance is linear. Account A will have a greater balance in Year 3. Then the correct option is B.

What is the slope?

The slope is the ratio of rising or falling and running. The difference between the ordinate is called rise or fall and the difference between the abscissa is called run.

The slope of the line is given as,

m = (y₂ - y₁) / (x₂ - x₁)

The slope for account A is calculated as,

m = (504 - 450) / (1 - 0) = (564 - 504) / (2 - 1)

54 ≠ 60

Account A is non-linear. The amount after 3 years will be more than $620 ($564 + $60).

The slope for account B is calculated as,

m = (570 - 550) / (1 - 0) = (590 - 570) / (2 - 1)

20 = 20

Account A is linear. The amount after 3 years will be $610 ($590 + $20).

More about the slope link is given below.

https://brainly.com/question/3605446

#SPJ2

What is the slope of the line that contains these points? x=9,13,17,21 and y =-24,-21,-18,-15

Answers

Slope: 3/4
...................

4(3x+2y) distributive property pls help

Answers

Answer:

[tex]12x+8y[/tex]

Step-by-step explanation:

1) Expand by distributing terms.

[tex]4*3x+4*2y[/tex]

2) Simplify 4*3x to 12x.

[tex]12x+4*2y[/tex]

3) Simplify  4*2y to 8y.

[tex]12x+8y[/tex]

Therefor, the answer is 12x + 8y.

NEED HELP ASAP WILL GIVE BRAINLY

Answers

Answer:

The third one

Step-by-step explanation:

4 x 14.4^3 x pi

---------------------

         3

Answer in a flash!!!

Answers

Answer:

C

Step-by-step explanation:

As x moves towards infinity, the y value is constant, it never changes.

Answer:

The answer is C, it doesn't show a change

Find the missing side

Answers

Answer:

8

Step-by-step explanation:

13 - 5 = 8


Find the value of x.

Answers

Answer:

x = 33

Step-by-step explanation:

x - 12 and 2x + 3 form a right angle , then

x - 12 + 2x + 3 = 90

3x - 9 = 90 ( add 9 to both sides )

3x = 99 ( divide both sides by 3 )

x = 33

Can some one help me answer this.

Answers

Answer: y= 0.0025

Step-by-step explanation:

Answer:

y= 0.0025

Step-by-step explanation:

every number in the y place is mutipled by four so to find y you need to divide 0.01 by 4

6)a garden was square, but last year she made it makes or shortening one side 5 meters and the other 8 meters. If the area of the smaller garden is 180 m², then what was the area of her square garden​

Answers

Answer:

let dimention of original garden be x

then (x-8)(x-5) = 180

x^2 -13x -140 = 0

(x-20)(x+7)=0

x= 20 or x = -7

x = 20

original area = (20)^2

= 400 m^2

The circumference of a circle measures 88 cm. Find the length of the circle's diameter Use pi = 22/7 PLS HELP MEEEEE

a) 8 cm
b) 276 cm
c) 44 cm
d) 28 cm

Answers

Answer:

28, let me know if you got it right

Determine the value of x (Different math problem)

Answers

Answer:

X=11

Step-by-step explanation:

5x+9+4x+5+7x-10=180°

5x+4x+7x+9+5-10=180°

16x+4=180°

16x=180°-4°

16x=176

X=11

HELP ME PLEASE!!,I WILL GIVE BRAINLIEST!!I PROMISE:)!!

Answers

Answer: C

The denominator is just the number on the bottom. In this case its [tex]2\sqrt{2}[/tex]

The area of a rectangular portrait is 20 square feet. It is 4 feet wide. How high is it?

Answers

Answer:

5 feet high

Step-by-step explanation:

A= LxW

Yx4= 20

  /4    /4

Y= 5ft

It is 5ft high

7,469.25 to the nearest cent

Answers

It already is to the nearest cent. 25 cents.

Answer:

0

Step-by-step explanation:

Marcus mows lawns for his summer job. He earns $15 per lawn. If he earned $75 dollars during the week, how many lawns did he mow?

Answers

Marcus mowed 5 lawns

Explanation: 75 divided by 15 = 5

What are two components of a sample space

Answers

i’m so sure, i’m sorry to :((

9r-5r+2+r ????????? Pls help me

Answers

Answer:

5r + 2

Step-by-step explanation:

9r-5r+2+r=5r+2

\mathrm{Group\:like\:terms}

=9r-5r+r+2

\mathrm{Add\:similar\:elements:}\:9r-5r+r=5r

=5r+2

Hiiioo can someone please help me with this ❤️❤️❤️

Answers

The answer is the third one 5/6

Also can I get brainliest plz

Please answer ASAP no links please and thank you

Answers

Answer:

28672

Step-by-step explanation:

4 x 4 x 4 x 4 x 7 x 4 x 4

One point on a line is (4, 6). The slope of the line is 3/4. Choose all of the following that could be another point on the line.
a. (0, 3)
b. (-8, -3)
c. (0, -3)
d. (-8, -1)
e. (12, 12)

Answers

The answer is d. I believe it was for mine

pls help will give brainliest

Answers

Answer:

Both classes will have the same value for the third quartile

Step-by-step explanation:

This is it because the 3rd quartile is where the maximum  or whisker is. Hope this helps!

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