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
Lunna [17]
2 years ago
7

Which is the equation of a hyperbola with directrices at x = ±2 and foci at (5, 0) and (−5, 0)? y squared over 40 minus x square

d over 10 equals 1 y squared over 10 minus x squared over 15 equals 1 x squared over 10 minus y squared over 40 equals 1 x squared over 10 minus y squared over 15 equals 1
Mathematics
1 answer:
N76 [4]2 years ago
6 0

The equation of the hyperbola with directrices at x = ±2 and foci at (5, 0) and (−5, 0) is \frac{x^2}{10} + \frac{y^2}{15} = 1

<h3>How to determine the equation of the hyperbola?</h3>

The given parameters are:

  • Directrices at x = ±2
  • Foci at (5, 0) and (−5, 0)

The foci of a hyperbola are represented as:

Foci = (k ± c, h)

The center is:

Center = (h,k)

And the directrix is:

Directrix, x = h ± a²/c

By comparison, we have:

k ± c = ±5

h = 0

h ± a²/c = ±2

Substitute h = 0 in h ± a²/c = ±2

0 ± a²/c = ±2

This gives

a²/c = 2

Multiply both sides by c

a² = 2c

k ± c = ±5 means that:

k ± c = 0 ± 5

By comparison, we have:

k = 0 and c = 5

Substitute c = 5 in a² = 2c

a² = 2 * 5

a² = 10

Next, we calculate b using:

b² = c² - a²

This gives

b² = 5² - 10

Evaluate

b² = 15

The hyperbola is represented as:

\frac{(x - k)^2}{a^2} + \frac{(y - h)^2}{b^2} = 1

So, we have:

\frac{(x - 0)^2}{10} + \frac{(y - 0)^2}{15} = 1

Evaluate

\frac{x^2}{10} + \frac{y^2}{15} = 1

Hence, the equation of the hyperbola is \frac{x^2}{10} + \frac{y^2}{15} = 1

Read more about hyperbola at:

brainly.com/question/3405939

#SPJ1

You might be interested in
Can someone please help with finding the surface area..
Vsevolod [243]

Answer:

it is 20.5

Step-by-step explanation:

you need to add all of the numbers together

5 0
3 years ago
Read 2 more answers
Either enter an exact answer in terms of \piπpi or use 3.14, point, 14 for \piπpi and enter your answer as a decimal.
OverLord2011 [107]

Answer:

49π sq. units

Step-by-step explanation:

Find the diagram attached

We can find the area of the given circle

Given

diameter of the circle d = 14

Area of the circle = πd²/4

Substitute the given diameter

Area of the circle = π(14)²/4

Area of the circle = 196π/4

Area of the circle = 49π sq. units

Hence the exact answer in terms of π is 49π sq. units

4 0
3 years ago
Can you solve 8/2(2+2)?
svetlana [45]

Answer:

1

Step-by-step explanation:

PEMDAS

2+2=4

2*4=8

8/8=1

6 0
3 years ago
Read 2 more answers
It is given that 3/7 , 12/m and n/49 are equivalent fractions. Find the value of ‘m’ and ‘n’.
denis23 [38]

Answer:

m=28

n=21

Step-by-step explanation:

3×4=12

7×4=28

28×1.75=49

12×1.75=21

4 0
3 years ago
5x-9&gt;4 and sketch a graph on that question​
iren [92.7K]

Answer:

Step-by-step explanation:

7 0
3 years ago
Other questions:
  • Aaron designed a robot for a contest. His robot can move 3/4 feet in 1/2 second. What is the robot’s unit rate of speed in miles
    5·1 answer
  • 15 3/4 divided by 1 3/4?
    15·1 answer
  • the library is 0.9 miles from school. the museum is 0.6 times as far from the school as the library. how far is the museum from
    10·2 answers
  • Factor 3xy+21x+9 completely
    6·1 answer
  • The measures of the angles of a triangle are shown in the figure below. Solve for x.<br> 80°<br> 39
    11·1 answer
  • I need help on math also thank you im not very smart...
    8·1 answer
  • Ashley will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $44 and costs an a
    8·1 answer
  • Henry buys an item for $4.23. He gives the cashier a $20 bill. How much money should Henry get back?
    10·1 answer
  • The turn signal Car A blinks 7 times every 5 seconds. The turn signal on Car B blinks 5 times every 4 seconds. In one minute, ho
    10·2 answers
  • Eva is solving the equation 4(x+32)=8
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!