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
mart [117]
3 years ago
14

X^2+4x+y^2-10y+20=30 find the center of the circle by completing the square

Mathematics
1 answer:
swat323 years ago
7 0

Answer:

a). Center of the circle = (-2, 5)

b). Equation of the line ⇒ y = -\frac{4}{5}x+\frac{58}{5}

Step-by-step explanation:

Equation of the circle is,

x² + 4x + y²- 10y + 20 = 30

a). [x² + 2(2)x + 4 - 4] + [y²- 2(5)y + 25] - 25 + 20 = 30

   [x² + 2(2)x + 4] - 4 + [y² - 2(5)y + 25] - 25 + 20 = 30

   (x + 2)² + (y - 5)²- 29 + 20 = 30

   (x + 2)² + (y - 5)²- 9 = 30

   (x + 2)² + (y - 5)² = 39

By comparing this equation with the standard equation of a circle,

    Center of the circle is (-2, 5).

b). A point (2, 10) lies on this circle.

    Slope of the line joining this point to the center (-2, 5),

    m_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}

          = \frac{10-5}{2+2}

          = \frac{5}{4}

    Let the slope of the tangent which is perpendicular to this line is 'm_{2}'

    Then by the property of perpendicular lines,

          m_{1}\times m_{2}=-1

          \frac{5}{4}\times m_{2}=-1

                 m_{2}=-\frac{4}{5}

   Now the equation of the line passing though (2, 10) having slope m_{2}=-\frac{4}{5}

           y - y' = m_{2}(x-x')

           y - 10 = -\frac{4}{5}(x-2)

           y - 10 = -\frac{4}{5}x+\frac{8}{5}

                  y = -\frac{4}{5}x+\frac{8}{5}+10

                  y = -\frac{4}{5}x+\frac{58}{5}

Therefore, equation of the line will be, y = -\frac{4}{5}x+\frac{58}{5}

You might be interested in
Help with 25,27,and 28
dedylja [7]

Answer:

For 25, the answer is C

Step-by-step explanation:

How I got the answer for 25 is:

To find the mean absolute deviation of the data, start by finding the mean of the data set.

How you do this is first you need to find the sum of the data values, (add all the numbers together) and divide the sum by the number of data values.(and divide that number by how many numbers you added together in the first place)

In this case, we'd be adding 44 + 39 + 47 + 38 + 38 + 41 + 40, and that equals 287. Now we'll divide 287 by how many numbers we added together, which is 7 numbers. 287 ÷ 7 = 41. That's the mean of the data set.

Next, we'll find the absolute deviation of the mean. How we do this is, we find how far away all the numbers are from 41.

44 is 3 away from 41

39 is 2 away from 41

47 is 6 away from 41

38 is 3 away from 41

41 is 0 away from 41

40 is 1 away from 41

So now, we add all of the distances together (3, 2, 6, 3, 0, and 1), and that equals 15! Now we do 15 ÷ 6, which is 2.5 and the reason we're dividing by 6 is because we're dividing by the number of distances we added together. Now, if you look on your worksheet, the closest answer to 2.5 is C, (2.6) so I'd chose that as the correct answer. I hope that helped!

4 0
3 years ago
Find the value of x.
777dan777 [17]
I dont get it look like you already did 
6 0
3 years ago
Greg kicked the soccer ball 75 feet .how many yards did he kick the ball
Sever21 [200]
Greg kicked it 25 yards
6 0
3 years ago
The sum of the digits of a two-digit number is 12. The number formed by reversing the digits is 54 more than the original number
andreyandreev [35.5K]

Answer:

39

Step-by-step explanation:

let the 2 digit number be ab = 10a + b ( considering place value )

The reversed  2 digit number is ba = 10b + a

The sum of the 2 digit number is

a + b = 12 ( subtract b from both sides )

a = 12 - b → (1)

Expressing as an equation

ba = ab + 54 , that is

10b + a = 10a + b + 54

Substitute a = 12 - b into the equation

10b + 12 - b = 10(12 - b) + b + 54 , simplify both sides

9b + 12 = 120 - 10b + b + 54

9b + 12 = - 9b + 174 ( add 9b to both sides )

18b + 12 = 174 ( subtract 12 from both sides )

18b = 162 ( divide both sides by 18 )

b = 9

Substitute b = 9 into (1)

a = 12 - 9 = 3

Thus

the original 2 digit number = ab = 39

The reversed 2 digit number = ba = 93

which is 54 more than the original number

7 0
3 years ago
Find the sales tax,, selling price: $40, rate of sales tax: 4%
JulijaS [17]
$1.60 is the answer. Just multiply 40 by .04 and you'll get 1.6.
4 0
3 years ago
Other questions:
  • Show that if n is an integer and n^3 + 5 is odd then n is even
    12·1 answer
  • The diagonals of a rhombus are 8 and 10 . the area of the rhombus is<br> 20<br> 40<br> 80
    7·2 answers
  • EXPERTS/ACE/GENIUSES
    8·1 answer
  • Find the value of x.
    13·1 answer
  • The prime factorization of GCF (18, 30)=
    14·1 answer
  • 3. Growth of Cholera bacteria. Suppose that the cholera bacteria in a colony grows unchecked according to the Law of Exponential
    15·1 answer
  • ⚠️⚠️⚠️⚠️⚠️HELP HELP HELP HELP PLEASEEEE I HAVE 7 MINUTES LEFT ⚠️⚠️⚠️⚠️⚠️
    8·1 answer
  • Find x if 2, 6 , x are in continued proportion
    15·1 answer
  • How can you decide which operation to use to solve a problem?
    14·1 answer
  • Hehehejejwjjejejjejejwkwkwkekekejjeue
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!