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
elena-14-01-66 [18.8K]
1 year ago
6

Find the center and radius of the circle

Mathematics
2 answers:
oksian1 [2.3K]1 year ago
6 0
<h2>Centre: </h2>

  • The general formula for the circumference is:

\boxed{ \boxed{{x^{2} \:  +  \: y ^{2}  \: +  \: Dx  \: + \:  Ey  \: + F \:  =  \: 0}}}

________________________

To find the center, write this formula:

\boxed{ \boxed{C( \frac{-D}{2} ,  \frac{-E}{2} )}}

____________________

<h3>We know that...</h3>

D \: = \: -6  \\  E \: = \: 4  \\  F \: = \: 4

We use the equation of the center with the values already obtained:

C( \frac{- - 6}{2} ,  \frac{-4}{2} )

C( \frac{6}{2} ,  \frac{-4}{2} )

\huge\boxed{ \bold{C( 3,   - 2 )}}

_____________________

<h2>Ratio: </h2>

Now we use the equation of the radius for a circumference, which is:

\boxed{ \boxed{{r \:  =  \:  \frac{1}{2}  \sqrt{D ^{2}  \:  +  \: E ^{2} \:  -  \: 4F } }}}

___________________________

Now we use the equation of the radius for a circumference with the values already obtained.

r \:  =  \:  \frac{1}{2}  \sqrt{  { - 6}^{2}  \:  +  \:  {4}^{2}  \:  -  \: 4 \:  \times  \: 4 }

  • I am going to use complex numbers because the square root of a negative number does not exist in the set of real numbers.

r \:  =  \:  \frac{1}{2}  \sqrt{  { - 6}^{2}  \:   -   \:  {4}^{2}  \:  - +  \: 4 \:  \times  \: 4 i}

r \:  =  \:  \frac{1}{2}  \sqrt{  {  6}^{2}  \:   -   \:  {4}^{2}  \:   +  \: 16i}

r \:  =  \:  \frac{ \sqrt{ {6}^{2} \:  -  \:  {4}^{2}   \:  +  \: 16i} }{2}

r \:  =  \:  \frac{ \sqrt{36 \:  -  \: 16 \:  +  \: 16i} }{2}

r \:  =  \:   \frac{ \sqrt{36i} }{2}

r \:  =  \:  \frac{6i}{2}

\huge \boxed{ \bold{r \:  =  \: 3i}}

<h3><em><u>MissSpanish</u></em></h3>

Wewaii [24]1 year ago
3 0
<h2><u>AnswEr </u><u>:</u></h2>

Provided Equation

  • x² + y² - 6x + 4y + 4= 0

As we know the Standard Equation of a Circle is

\bf{(x - a)} {}^{2}  + (y - b) {}^{2}  =  {r}^{2}

where,

r radius of circle.

(a,b) centre .

\implies \sf \:  {x}^{2}  +  {y}^{2}  - 6x + 4y + 4 = 0

This equation can be further written as

\implies \sf \:  {x}^{2}   - 6x +   {y}^{2}   + 4y  =  - 4

Now completing the square ( by adding 4 & 9 on both side ) .

\implies \sf \:  {x}^{2}   - 6x +  9 +  {y}^{2}   + 4y  + 4  =  - 4 + 9  + 4

again this equation can be further written as

\implies \sf \: (x - 3) {}^{2}  + (y + 2) {}^{2}  =  {3}^{2}

Now comparing this equation with standard equation of circle ( mentioned above) and we will get

  • Centre = ( a,b) = (3, -2 )
  • Radius = r = 3

Therefore,

  • <u>Centre </u><u>of </u><u>circle </u><u>is </u><u>(</u><u>3</u><u>,</u><u>-</u><u>2</u><u>)</u><u> </u><u>and </u><u>radius </u><u>is </u><u>3</u>
You might be interested in
A sphere is just enclosed inside a right circular cylinder. If the volume of the sphere is 140 cm3, find the volume of the gap b
alexgriva [62]
-----------------------------------------------------------
Find Radius :
-----------------------------------------------------------
\text {Volume of a sphere =}   \dfrac{4}{3}  \pi r^3

\dfrac{4}{3}  \pi r^3 = 140

\pi r^3 = 140 \times  \dfrac{3}{4}

\pi r^3 = 105

r^3 =  \dfrac{105}{ \pi}

r = 3.22 \ cm

-----------------------------------------------------------
Find volume of the cylinder :
-----------------------------------------------------------
\text {Volume of the cylinder = } \pi r^2h

\text {Volume of the cylinder = } \pi ((3.22)^2(3.22 \times 2)

\text {Volume of the cylinder = } 209.77 \ cm^3

-----------------------------------------------------------
Find volume of the gap :
-----------------------------------------------------------
\text {Volume of gap = } 209.77 - 140

\text {Volume of gap = } 69.77 \ cm^3

-----------------------------------------------------------
\bf \text {Answer : } 69.77 \cm^3
-----------------------------------------------------------

6 0
3 years ago
Factor gcf 5ab^2 + 10ab
Mrrafil [7]
<span>5ab^2 + 10ab

5ab^2 = 5ab *(b)
10ab = 5ab *(2)

so GCF of </span>5ab^2 + 10ab = 5ab
4 0
3 years ago
Read 2 more answers
Given The following Graph:<br><br> a.)Evaluate f(0). <br> b.) Solve for f(x) = -3
dlinn [17]

Answer:

see explanation

Step-by-step explanation:

a

f(0) means find the value of y when x = 0

That is f(0) = 1 ← the point (0, 1) on the graph

b

When f(x) = - 3 means what are the values of x corresponding to y = - 3

From the graph when y = - 3 there are 2 corresponding values of x, that is

x = - 2 or x = + 2

The solution to f(x) = - 3 is x = ± 2

3 0
4 years ago
X²+7x+10=0 a=1, b=7, c=10 b²-4ac=(7)²-4(1) (10) =49-4(10) =49-40 =9​
Sloan [31]

Answer:

X=5

X=2

Step-by-step explanation:

8 0
3 years ago
What is another way to write the ratio 13 to 6
Mashutka [201]

Answer:

Step-by-step explanation:

13:6

5 0
3 years ago
Other questions:
  • Andre and scott share the driving on a trip. Scott drives 7 miles more than three times tge distance Andre drives. If the trip i
    13·2 answers
  • Figure 1 is dilated to get Figure 2.
    15·2 answers
  • 2x+4x=3x+1 how do you do this
    8·1 answer
  • In how many distinct ways can the letters in engineering be arranged?
    8·2 answers
  • Can someone explain to me 4(7q+3)
    12·2 answers
  • Wich fraction is equivalent to 2/8
    8·2 answers
  • Cari is searching online for airline tickets. Two weeks ago, the cost to fly from Boston to Denver was $225. Now the cost is $30
    12·1 answer
  • PLEASE HELP, ILL GIVE YOU 15
    11·1 answer
  • What is 10^x=1/100?<br> solve for x
    13·1 answer
  • Please help me i need it fast
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!