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
xxTIMURxx [149]
2 years ago
5

Select the correct answer. which hyperbola has both foci lying in the same quadrant? a. b. c. d.

Mathematics
1 answer:
faltersainse [42]2 years ago
7 0

The hyperbola having both foci lying in the same quadrant is <u>(y - 16)²/9² - (x + 1)²/12² = 1</u>, making the <u>4th option</u> a right choice.

For the hyperbola with an equation of the form (x - h)²/a² - (y - k)²/b² = 1, the foci in on the points (h + c, k) and (h - c, k), where c = √(a² + b²).

For the hyperbola with an equation of the form (y - k)²/a² - (x - h)²/b² = 1, the foci in on the points (h, k + c) and (h, k - c), where c = √(a² + b²).

<u>Among the options</u>:

(a) (x - 24)²/24² - (y -1)²/7² = 1.

The equation is of the form (x - h)²/a² - (y - k)²/b².

h = 24, k = 1, a = 24, b = 7.

c = √(a² + b²) = √(24² + 7²) = √(576 + 49) = √625 = 25.

Thus, foci are at the points (h + c, k), (h - c, k) = (24 + 25, 1), (24 - 25, 1) = (49, 1), and (-1, 1), which are in different quadrants.

(b) (y - 12)²/5² - (x - 6)²/12² = 1.

The equation is of the form (y - k)²/a² - (x - h)²/b².

h = 6, k = 12, a = 5, b = 12.

c = √(a² + b²) = √(5² + 12²) = √(25 + 144) = √169 = 13.

Thus, foci are at the points (h, k + c), (h, k - c) = (6, 12 + 13), (6, 12 - 13) = (6, 25), and (6, -1), which are in different quadrants.

(c) (y - 16)²/15² - (x - 2)²/8² = 1.

The equation is of the form (y - k)²/a² - (x - h)²/b².

h = 2, k = 16, a = 15, b = 8.

c = √(a² + b²) = √(15² + 8²) = √(225 + 64) = √289 = 17.

Thus, foci are at the points (h, k + c), (h, k - c) = (2, 16 + 17), (2, 16 - 17) = (2, 33), and (2, -1), which are in different quadrants.

(d) (y - 16)²/9² - (x + 1)²/12² = 1.

The equation is of the form (y - k)²/a² - (x - h)²/b².

h = -1, k = 16, a = 9, b = 12.

c = √(a² + b²) = √(9² + 12²) = √(81 + 144) = √225 = 15.

Thus, foci are at the points (h, k + c), (h, k - c) = (-1, 16 + 15), (-1, 16 - 15) = (-1, 31), and (-1, 1), which are in the same quadrants (QUADRANT II).

Thus, the hyperbola having both foci lying in the same quadrant is <u>(y - 16)²/9² - (x + 1)²/12² = 1</u>, making the <u>4th option</u> a right choice.

Learn more about the foci of a hyperbola at

brainly.com/question/9384729

#SPJ4

For the options, refer the image.

You might be interested in
PLEASE HELP ME If 0 &lt; z ≤ 90 and sin(9z − 1) = cos(6z + 1), what is the value of z? z = 3 z = 4 z = 5 z = 6
Burka [1]

Answer:

  z = 6

Step-by-step explanation:

We know that ...

  sin(x) = cos(90 -x)

Substituting (9z-1) for x, this is ...

  sin(9z -1) = cos(90 -(9z -1))

But we also are given ...

  sin(9z -1) = cos(6z +1)

Equating the arguments of the cosine function, we have ...

  90 -(9z -1) = 6z +1

  90 = 15z . . . . . . . . . add (9z-1) to both sides

  6 = z . . . . . . . . . . . . divide by 15

_____

<em>Comment on the graph</em>

The attached graph shows 5 solutions in the domain of interest. These come from the fact that the relation we used is actually ...

  sin(x) = cos(90 +360k -x)  . . . . .  for any integer k

Then the above equation becomes ...

  90 +360k = 15z

  6 +24k = z . . . . . . . . . for any integer k

The sine and cosine functions also enjoy the relation ...

  sin(x) = cos(x -90)

  sin(9z -1) = cos(9z -1 -90) = cos(6z +1)

  3z = 92 . . . . . equating arguments of cos( ) and adding 91-6z

  z = 30 2/3

6 0
3 years ago
Could use some help!
Natasha_Volkova [10]


[6, ∞) , x >= 6 so

answer is D. last one

6<= x < ∞
6 0
3 years ago
X/19 = 4 <br> what is x please help i don`t under stand this equation <br> p.s. xover 19 =4
ivann1987 [24]
The answer is 76 i think
8 0
2 years ago
1 cat + 20 dogs + 60 men + 5 shark=​
Goryan [66]

Answer:

Step-by-step explanation:

1 cat + 20 dogs + 60 men + 5 shark=​ 86

6 0
3 years ago
Read 2 more answers
Solve each equation for x
Andrews [41]
BY taking the square root you can find each of them as follows:

1. sqrt(144) = 12

2. sqrt(25/289) = 5/17
6 0
3 years ago
Other questions:
  • Find the two integers, m and n,<br><br> make the equation (2x^ny2)m = 4x6y4 true.
    12·1 answer
  • Which situation describes using a credit card? A. Jackie asked a bank teller to withdraw cash for her. B. Cory bought a book, an
    15·1 answer
  • I need help on this question
    15·1 answer
  • How could you test if a number is divisible by 12 15 or 24
    11·1 answer
  • Write 2^60 as an exponent with a base of: 4 , 16<br><br><br> pls explain why you got it, thx!
    9·1 answer
  • Brainliest is gained by answering this word problem.
    6·1 answer
  • On a map, the distance between Dallas, TX and Memphis, TN is 57.5 cm. What is the actual distance if the map scale is 1 cm:8 mi.
    10·1 answer
  • Find the 8th term of the arithmetic sequence -5x+3, x+9, 7x+15, ...
    8·1 answer
  • 4. An account was opened with $3000 earning 5%
    13·1 answer
  • A company's sales equal $60,000 and cost of goods sold equals $20,000. Its beginning inventory was $1,600 and its ending invento
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!