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
sleet_krkn [62]
3 years ago
13

Which is the equation of a hyperbola centered at the origin with x-intercept +\- 3 and asymptote y=2x

Mathematics
1 answer:
Radda [10]3 years ago
7 0

Answer:

{\dfrac{x^{2}}{9} - \dfrac{y^{2}}{36} = 1}

Step-by-step explanation:

The hyperbola has x-intercepts, so it has a horizontal transverse axis.

The standard form of the equation of a hyperbola with a horizontal transverse axis is  \dfrac{(x - h)^{2}}{a^{2}} - \dfrac{(y - k)^{2}}{b^{2}} = 1

The center is at (h,k).

The distance between the vertices is 2a.

The equations of the asymptotes arey = k \pm \dfrac{b}{a}(x - h)

1. Calculate h and k. The hyperbola is symmetric about the origin, so  

h = 0 and k = 0

2. For 'a': 2a = x₂ - x₁ = 3 - (-3) = 3 + 3 = 6

a = 6/2 = 3  

3. For 'b': The equation for the asymptote with the positive slope is  

y = k + \dfrac{b}{a}(x - h) = \dfrac{b}{a}x

Thus,  asymptote has the slope of

\begin{array}{rcl}m& =& \dfrac{b}{a}\\\\2& =& \dfrac{b}{3}\\\\b& =& \mathbf{6}\end{array}

4.  The equation of the hyperbola is

\large \boxed{\mathbf{\dfrac{x^{2}}{9} - \dfrac{y^{2}}{36} = 1}}

The attachment below represents your hyperbola with x-intercepts at ±3 and asymptotes with slope ±2.

You might be interested in
Please help ASAP 25 pts + brainliest to right/best answer
zhuklara [117]

Answer:


Step-by-step explanation:

LOGb(x)=y

4^5=1024

= log(4)1024=5

4 0
3 years ago
What is the ratio of boys to girls, in lowest terms, if the number of boys is 45 and the number of girls is 33?
Nastasia [14]
It is 15/11 i hope i'm right


5 0
3 years ago
Carlos takes classes at both Westside Community College and Pinewood Community College. At Westside, class fees are $ 98 per cre
Sholpan [36]

Answer:

x + y = 13

98x + 115y = z

Step-by-step explanation:

Let x represent the time spent taking class in Westside community college

Let y represent the time spent taking class in Pinewood community college

Let z represent the combined total amount paid for the class fees.

The total combined time for the two school is given as:

x + y = 13.

For the combined total amount; we multiply the price for each school with the time spent on the school and sum them together.

Westside: 98 * x = 98x

Pinewood: 115 * y = 115y

The combined total amount represented as z is given as:

z = 98x + 115y

7 0
3 years ago
Here's a easy one<br> Not accepting links!
irakobra [83]
Wwhhaatt??? I have no idea what your question is.
5 0
3 years ago
Which two equations can you use to find the adult and child admission fees for a puppet show? Let a represent the fee for adults
vlabodo [156]

45a + 30c = 315 \\ 50a + 40c = 370
The answers are C and E

Hope this helps. - M
3 0
3 years ago
Read 2 more answers
Other questions:
  • Can some one help me with math
    10·2 answers
  • How do I solve this complex multi-step equation 2x + (-2 )= 10x - 4 ?
    10·2 answers
  • State the degree of the polynomial.
    10·1 answer
  • Please help me on a test 2 3/4 + 5 1/2
    5·1 answer
  • 14. The following solution contains errors. Identify the errors and explain why they are incorrect.
    13·1 answer
  • URGENT WILL GIVE BRAINLIEST
    15·1 answer
  • What is the answer tox+5&lt;-12
    13·2 answers
  • Item 1
    12·1 answer
  • Which Exponentail expression represents The numerical expression 1/12 . 1/12 . 1/12 . 1/12?
    12·1 answer
  • Which equation has no solutions?<br> 0 32 +2= 4x + 2<br> 0 32 +2= 20<br> 0 32 +2=42<br> 0 32 +2=2
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!