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
KonstantinChe [14]
3 years ago
11

Find an equation in standard form for the hyperbola with vertices at (0, ±10) and asymptotes at y = ±five divided by four times

x..
Mathematics
1 answer:
Vinvika [58]3 years ago
5 0

Answer:

The equation of the hyperbola in standard form is

\frac{y^{2}}{100}-\frac{4x^{2}}{625}=1

Step-by-step explanation:

* We will take about the standard form equation of the hyperbola

- If the given coordinates of the vertices (0 , a) and (0 , -a)

∴ The transverse axis is the y-axis. (because x = 0)

- If the given asymptotes at y = ± (b/a) x

∴  Use the standard form  ⇒ y²/a² - x²/b² = 1

* Lets use this to solve our problem

∵ The vertices are (0 , 10) and (0 , -10)

∴ a = ±10

∴ a² = 100

∵ The asymptotes at y = ± 5/4 x

∴ ± 5/4 = ± b/a

∵ a = ± 10

∴ ± 5/4 = ± b/10 ⇒ using cross multiplication

∴± (4b) = ± (5 × 10) = ± 50 ⇒ divide both sides by 4

∴ b = ± 25/2

∴ b² = 625/4

* Now Lets write the equation

* y²/100 - x²/(625/4) = 1

∵ x² ÷ 625/4 = x² × 4/625 = (4x²/625)

∴ y²/100 - 4x²/625 = 1

* The equation of the hyperbola in standard form is

  \frac{y^{2}}{100}-\frac{4x^{2}}{625}=1

You might be interested in
What is the answer to this problem
Aleks04 [339]

Answer:

14 cm^2

Step-by-step explanation:

You find the area of both triangles, and subtract by 4

6x3x1/2x2 - 2x2

18 - 4

14

3 0
2 years ago
Determine whether the triangles are similar. If they are, state how (AA , SSS, SAS -). And choose the correct similarity stateme
velikii [3]

Answer:

WHAT THE FRACTION IS THIS!!!!

Step-by-step explanation:

i dont know what kind of math this is but this takes geomatry and mathematical observations to get it correct.

4 0
3 years ago
The half-life of chromium-51 is 28 days. If the sample contained 5.10 grams, how much chromium was present 168 days ago?
stepan [7]
I don’t understand how many grams had the first one,so I can’t help you
3 0
2 years ago
The temperature of a city is recorded at midnight on the last days of four consecutive months
Serhud [2]

Answer:

26 degrees Celcius

Step-by-step explanation:

The minimum temperature is -11

The maximum temperature is 15

to get from -11 to 0: add 11

to get from 0 to 15: add 15

11+15 = 26

6 0
2 years ago
Multiply the decimal numbers 37.4 x 2.2 =
Advocard [28]
Basically you multiply like normal and then add in the decimal point (to figure out where it goes count how many numbers are behind the decimal (in this case 2) and then count that many places from the right into your answer and that's where it goes). So here 374 x22 =8228 but when you add in the decimal you get 82.28 :)
7 0
2 years ago
Read 2 more answers
Other questions:
  • which of the ordered pairs is a solution of the following equation? y = -2x + 4 choose an answer A) (0,4) or B) (2,2) or C) (4,0
    6·2 answers
  • If y varies directly as the x^2 and y = 200 when x = 5, what is the value of y when x = -3?
    6·1 answer
  • What is the solution to 2x-8<12
    13·1 answer
  • What’s the y = to ???
    9·1 answer
  • Solve for x² in x²-3x+2=0​
    11·2 answers
  • The equations in the system below are parallel.
    10·1 answer
  • The diagram is not drawn to scale<br><br> Find the value of x.
    13·1 answer
  • Which is the graph of y=-x-3?
    8·1 answer
  • Abe ate 1/6 of a small pizza. Aisha ate 1/8 of a small pizza. Who ate more?
    7·1 answer
  • How do I find and round the principal square root of 8​
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!