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
user100 [1]
3 years ago
6

The center of a hyperbola is located at the origin. One focus is located at (−50, 0) and its associated directrix is represented

by the line x= 2.304/50. What is the equation of the hyperbola?
Mathematics
2 answers:
SOVA2 [1]3 years ago
6 0

Answer:

The answwr is A

Step-by-step explanation:

leva [86]3 years ago
5 0

The equation of the hyperbola is : \frac{x^{2}}{48^2}  - \frac{y^{2}}{14^2}  = 1

The center of a hyperbola is located at the origin that means at (0, 0) and one of the focus is at (-50, 0)

As both center and the focus are lying on the x-axis, so the hyperbola is a horizontal hyperbola and the standard equation of horizontal hyperbola when center is at origin: \frac{x^{2}}{a^{2}}  - \frac{y^{2}}{b^{2}}    = 1

The distance from center to focus is 'c' and here focus is at (-50,0)

So, c= 50

Now if the distance from center to the directrix line is 'd', then

d= \frac{a^{2}}{c}

Here the directrix line is given as : x= 2304/50

Thus, \frac{a^{2}}{c}  = \frac{2304}{50}

⇒ \frac{a^{2}}{50}  = \frac{2304}{50}

⇒ a² = 2304

⇒ a = √2304 = 48

For hyperbola, b² = c² - a²

⇒ b² = 50² - 48² (By plugging c=50 and a = 48)

⇒ b² = 2500 - 2304

⇒ b² = 196

⇒ b = √196 = 14

So, the equation of the hyperbola is : \frac{x^{2}}{48^2}  - \frac{y^{2}}{14^2}  = 1

You might be interested in
What value of n makes the equation true?
goldenfox [79]

Answer:

n=10

Step-by-step explanation:

You need n to be 10 because: y^20= (y^10)^2

4 0
3 years ago
Read 2 more answers
Solve the following system by any method -8x-8y=0 -8x+2y=-20
iVinArrow [24]
                     \fbox{Solution by using Matrix} 

\text{Linear Equation} = -8x-8y=0 , -8x+2y=-20

\text{Rewrite the linear equations above as a matrix} 

\left[\begin{array}{ccc}8&-8&0\\-8&2&-20\\\end{array}\right] 

\text{Apply to Row2 : Row2 + Row1} 

\left[\begin{array}{ccc}8&-8&0\\-8&-6&-20\\\end{array}\right] 

\text{ Simplify rows} 

\left[\begin{array}{ccc}8&-8&0\\0&1&10/3\\\end{array}\right] 

\text{Note: The matrix is now in echelon form.}\text{The steps below are for back substitution.} 

\text{Apply to Row1 : Row1 + 8 Row2} 

\left[\begin{array}{ccc}8&0&80/30\\0&1&10/3\\\end{array}\right] 

\text{ Simplify rows}  

\left[\begin{array}{ccc}1&0&10/3\\0&1&10/3\\\end{array}\right] 

\text{Therefore, the solution is} 

x= \dfrac{10}{3} \ \text{and} \ \ y=\dfrac{10}{3}
7 0
3 years ago
Expand and Simplify <br> 4( b+3) + 2 (b + 5)
Ipatiy [6.2K]

Answer:

4( b+3) + 2 (b + 5)

4b+12+2b+10

6b+22

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
HELP I NEED HELP ASAP
My name is Ann [436]

Answer: is C

Step-by-step explanation:

7 0
3 years ago
The difference of the present ages of two sister in 5 yrs
Gekata [30.6K]

Answer:

4 and 9

Step-by-step explanation:

let their ages be x and x - 5, then in 4 years their ages will be

x + 4 and x - 5 + 4 = x - 1 , and the product is 104, thus

(x + 4)(x - 1) = 104 ← expand factors on left using FOIL

x² + 3x - 4 = 104 ( subtract 104 from both sides )

x² + 3x - 108 = 0 ← in standard form

(x + 12)(x - 9) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 12 = 0 ⇒ x = - 12

x - 9 = 0 ⇒ x = 9

However, x > 0 ⇒ x = 9

Thus

Their present ages are 9 and 9 - 5 = 4

4 0
3 years ago
Other questions:
  • HELP PLEASE
    12·2 answers
  • 10 times 10 times 10 <br> exponent form:<br> word form:
    9·2 answers
  • Find the midpoint of the segment with the following endpoints.<br> (5,9) and (0,3)
    9·2 answers
  • Solve u² = 49, where u is a real number.<br> Simplify your answer as much as possible.
    15·1 answer
  • 1. What are the four orders of operations
    12·2 answers
  • Domenic and Adriana are observing a hot-air balloon from two tracking stations on the ground.
    13·1 answer
  • A credit card issuer charges an APR of 13.99%, and its billing cycle is 30 days long. What is its periodic interest rate?
    12·2 answers
  • CAN SOMEONE HELP ME W THIS FASTTTT I NEED HELP HELPPP​
    6·2 answers
  • What is
    11·2 answers
  • What is the value of x
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!