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
tankabanditka [31]
2 years ago
8

Identify the standard form of the equation by completing the square.

Mathematics
1 answer:
OLEGan [10]2 years ago
4 0

Answer:

\dfrac{(x-1)^2}{9}-\dfrac{(y-2)^2}{4}=1

Step-by-step explanation:

<u>Given equation</u>:

4x^2-9y^2-8x+36y-68=0

This is an equation for a horizontal hyperbola.

<u>To complete the square for a hyperbola</u>

Arrange the equation so all the terms with variables are on the left side and the constant is on the right side.

\implies 4x^2-8x-9y^2+36y=68

Factor out the coefficient of the x² term and the y² term.

\implies 4(x^2-2x)-9(y^2-4y)=68

Add the square of half the coefficient of x and y inside the parentheses of the left side, and add the distributed values to the right side:

\implies 4\left(x^2-2x+\left(\dfrac{-2}{2}\right)^2\right)-9\left(y^2-4y+\left(\dfrac{-4}{2}\right)^2\right)=68+4\left(\dfrac{-2}{2}\right)^2-9\left(\dfrac{-4}{2}\right)^2

\implies 4\left(x^2-2x+1\right)-9\left(y^2-4y+4\right)=36

Factor the two perfect trinomials on the left side:

\implies 4(x-1)^2-9(y-2)^2=36

Divide both sides by the number of the right side so the right side equals 1:

\implies \dfrac{4(x-1)^2}{36}-\dfrac{9(y-2)^2}{36}=\dfrac{36}{36}

Simplify:

\implies \dfrac{(x-1)^2}{9}-\dfrac{(y-2)^2}{4}=1

Therefore, this is the standard equation for a horizontal hyperbola with:

  • center = (1, 2)
  • vertices = (-2, 2) and (4, 2)
  • co-vertices = (1, 0) and (1, 4)
  • \textsf{Asymptotes}: \quad y = -\dfrac{2}{3}x+\dfrac{8}{3} \textsf{ and }y=\dfrac{2}{3}x+\dfrac{4}{3}
  • \textsf{Foci}: \quad  (1-\sqrt{13}, 2) \textsf{ and }(1+\sqrt{13}, 2)

You might be interested in
What is 1.3 repeating as a mixed number?
photoshop1234 [79]
The answer would 
 be 13/10
5 0
3 years ago
What is the solution to the equation 3(y-2)=2y-8 A.-2/5 B.-14 C. -2 D. -2 4/5 I NEED-HELP PLeAse
AlladinOne [14]

3(y - 2) = 2y - 8

3y - 6 = 2y - 8

3y - 2y = -8 + 6

y = -2

Answer: C

4 0
3 years ago
Help plz!!!!!!!!!!!!!!!!!!!!
RUDIKE [14]
4 Triangles 1/2(6)6()= 18 18x4= 72
5 squares 3X3=9. 5x9= 45

72+45= 117 sq in
5 0
3 years ago
please help me to solve both question.....need your help....N33d your working...i swear i will mark brainliest who answer it♥♥♥​
emmasim [6.3K]

Answer:

Hello. The answer is 250.

Step-by-step explanation:

The explanation takes alot of time

The two important tips are

Sum of the interior angles of triangle is 180

And for those which have 4 sides are 360

4 0
3 years ago
What is special about y coordinate that goes with the x coordinate of 1on a proportional gragh
Rom4ik [11]

Answer:

The first coordinate (usually the x-coordinate) is called the domain and the second (usually the y-coordinate) is called the range. If tou remember from earlier chapters the domain contains values that correspond to the independent variable whereas the range contains values corresponding to the dependent variable.

Step-by-step explanation:

I majored in Mathematics

4 0
3 years ago
Other questions:
  • When you add a positive number and a negative, how
    7·1 answer
  • How to graph 5x-5y=20
    7·1 answer
  • Find the value of x and if necessary, express answer in simplest radical form.
    6·1 answer
  • Which is greater 3/7 3/6 3/5
    14·2 answers
  • 5. In the figure, . Solve for . Show your work.
    6·1 answer
  • Write this number in standard form four and thirty one hundreths
    8·1 answer
  • What fraction is greater 1/2 or 6/11
    13·1 answer
  • A hockey player takes 150 shots each week. Sixty percent of these shots go in. How many shots do NOT go in?
    11·1 answer
  • Which equation is true?
    15·1 answer
  • Which net represents this rectangular prism?
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!