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
PIT_PIT [208]
3 years ago
15

Find hyperbola equation. center (0,0) vertex (-2,0) focus (-5,0)

Mathematics
1 answer:
r-ruslan [8.4K]3 years ago
4 0

\frac{ {x}^{2} }{4}  -  \frac{ {y}^{2} }{21}  = 1

<h2 />

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

<h3>a= (–2, 0) ; Center =(0,0)</h3>

<h3>distance =  \sqrt{(x2 - x1)^{2} + (y2 - y1) ^{2}  }  \\ a =  \sqrt{(( - 2) - 0)^{2} + (0 - 0) ^{2}  }  \\ a =  \sqrt{ {2}^{2} }  \\ a = 2</h3><h3>C = (–5,0) ; Center =(0,0)</h3>

distance = \sqrt{(x2 - x1) ^{2} + (y2 - y1) ^{2}  }  \\ c =  \sqrt{(( - 5)  - 0)^{2}  + (0 - 0) ^{2} }  \\ c =  \sqrt{ {5}^{2} }  \\ c = 5

<h3>C²= a²+ b²</h3><h3>(5)²= (2)² + b²</h3><h3>b²= 25–4 —> b² = 21 </h3>

b =   + \sqrt{21} , -  \sqrt{21}

m =  \frac{y2 - y1}{x2 - x1}  =  \frac{0 - 0}{0 - ( -5 )}  = 0

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

\frac{(x - 0)^{2} }{ {2}^{2} }  -  \frac{(y - 0) ^{2} }{ { \sqrt{2} }^{2} }  = 1 \\

\frac{ {x}^{2} }{4}  -  \frac{ {y}^{2} }{21}  = 1

I hope I helped you^_^

You might be interested in
A blueprint for a house has a scale of 1: 40. A wall in the blueprint is 3 in. What is the length of the actual wall?
Svetradugi [14.3K]

The length is 120 feet. Setting up a proportion, you get 1/40=3/x. Solving for x, you get 120.


8 0
4 years ago
2 to the one fourth minus 3 to the fifth
Sauron [17]
2^4 = 16
3^5 = 243
16 - 243 = -227

3 0
4 years ago
How do you solve 5/x=x-4
alexandr402 [8]
\frac{5}{x}=x-4\\&#10;x\not=0\\&#10;5=x^2-4x\\&#10;x^2-4x-5=0\\&#10;x^2+x-5x-5=0\\&#10;x(x+1)-5(x+1)=0\\&#10;(x-5)(x+1)=0\\&#10;x=5 \vee x=-1
6 0
4 years ago
How much is this? <br>(1/2α+1/3)²​
zloy xaker [14]

Answer: 1/(4a^2) + 1/(3a) + 1/9

Step-by-step explanation:

= (1/2a + 1/3)(1/2a + 1/3)

= 1/(4a^2) + 1/(6a) + 1/(6a) + 1/9

= 1/(4a^2) + 2/(6a) + 1/9

= 1/(4a^2) + 1/(3a) + 1/9

8 0
3 years ago
Solve the solution. How many solutions does it have? 4(2x-3)=2(4x-6)
sdas [7]

Answer:

No solutions

Step-by-step explanation:

4(2x-3)=2(4x-6)

4(2x-3)=2 \times 2(2x-3) \\  \\ 4(2x-3)=4(2x-3)

Same components are present on both sides of equal sign, therefore NO SOLUTIONS are possible.

7 0
4 years ago
Other questions:
  • Who Washes? Erica and Aaron, who are siblings, have decided to use a lottery system to decide who will wash dishes every night.
    6·1 answer
  • 16/250, 6.5% and 0.062 from least to greatest
    10·1 answer
  • What is 5(6.2+z)z=3.8​
    14·1 answer
  • Which equation has a y-intercept at (0,3) and a x-intercept at (-4,0)
    11·1 answer
  • A number of eggs ,e, divide by 12
    14·1 answer
  • The average score on a standardized test is 500 points with a standard deviation of 50 points. What is the probability that a st
    15·1 answer
  • the probability that kimmy makes a basket is 7/10. if she shoots 150 baskets, how many can she expect to make?
    15·1 answer
  • Which problem solving strategy would be best to solve this problem? How far did you drive if you drove 2 hours at 55 miles per h
    15·1 answer
  • Which of the folowing is equal to 7 1/3
    6·1 answer
  • Show that
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!