1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Iteru [2.4K]
2 years ago
14

Need this badly!!!!!!

Mathematics
1 answer:
prohojiy [21]2 years ago
3 0
<h2>Hello!</h2>

The answer is:

The center of the circle is located on the point (-9,-2) and the radius is 6 units.

<h2>Why?</h2>

To solve the problem, we need to use the given equation which is in the general form.

We are given the circle:

x^{2}+y^{2}+18x+4y+49=0

We know that a circle can be written in the following form:

(x-h)^{2}+(y-k)^{2}=r^{2}

Where,

h is the x-coordinate of the center of the circle

k is the y-coordinate of the center of the circle

r is the radius of the circle.

So, to find the center and the radius, we need to perform the following steps:

- Moving the constant to the other side of the equation:

x^{2}+y^{2}+18x+4y=-49

- Grouping the terms:

x^{2}+18x+y^{2}+4y=-49

- Completing squares for both variables, we have:

We need to sum to each side of the equation the following term:

(\frac{b}{2})^{2}

Where, b, for this case, will the coefficients for both terms that have linear variables (x and y)

So, the variable "x", we have:

x^{2} +18x

Where,

b=18

Then,

(\frac{18}{2})^{2}=(9)^{2}=81

So, we need to add the number 81 to each side of the circle equation.

Now, for the variable "y", we have:

y^{2} +4y

Where,

b=4

(\frac{4}{2})^{2}=(2)^{2}=4

So, we need to add the number 4 to each side of the circle equation.

Therefore, we have:

(x^{2}+18x+81)+(y^{2}+4y+4)=-49+81+4

Then, factoring, we have that the expression will be:

(x+9)^{2}+(y+2)^{2}=36

- Writing the standard form of the circle:

Now,  from the simplified expression (after factoring), we can find the equation of the circle in the standard form:

(x+9)^{2}+(y+2)^{2}=36

Is also equal to:

(x-(-9))^{2}+(y-(-2))^{2}=36

Where,

h=-9\\k=-2\\r=\sqrt{36}=6

Hence, the center of the circle is located on the point (-9,-2) and the radius is 6 units.

Have a nice day!

You might be interested in
4 ones 4tenths + 4tenths
Black_prince [1.1K]

Answer:

86

Step-by-step explanation:

4 0
3 years ago
After a dilation with center (0,0) the image of DB is D’B’ if DB=6 and D’B’=2 the scale factor of dilation is what ?
bezimeni [28]

Answer:

scale factor = \frac{1}{3}

Step-by-step explanation:

the scale factor is the ratio of corrresponding sides. image to original.

scale factor = \frac{D'B'}{DB} = \frac{2}{6} = \frac{1}{3}

7 0
2 years ago
PLease answer 1, 2, and 3 so I can be free till december
Kobotan [32]
Is there a picture for this?
3 0
2 years ago
Can someone please help?
Dmitry_Shevchenko [17]

Answer:

A coordinate pair that works as a solution is (1,3)

5 0
3 years ago
Read 2 more answers
34− 6 × 3+ 78 pemdas
Mazyrski [523]

Answer:

94

Step-by-step explanation:

PEDMAS

34 - 6 \times 3 + 78 \\ 34 - 18 + 78 \\ 34 + 60 \\  = 94

Step 1 : Multiplication :

-6×3 =-18

Step 2: Addition: -18+78 = +60

Step 3: Addition : 35+60

= 94

8 0
3 years ago
Read 2 more answers
Other questions:
  • How do I simplify the following 1-4(u-1)
    5·1 answer
  • What is the slope of y=-4
    5·2 answers
  • What is 64 written as a product of the same factor
    5·2 answers
  • Player 1
    6·1 answer
  • I want answer for this one
    9·2 answers
  • Someone helpp commonn
    11·1 answer
  • Pls Help! Put a proper answer! If you put a link I will report you!
    14·1 answer
  • How much time has passed from the first clock to the second clock?
    9·1 answer
  • A student in a foreign language program learns 15 new words each week. Which graph best represents the relationship between x, t
    12·1 answer
  • Solve the following equation by first writing the equation in the form ax² = c
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!