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!!!!!!!!!!
Sergeu [11.5K]
1, 3, and 5 would be my best guesses but I’m not 100 percent sure
7 0
2 years ago
Simone has 20 bills. One fifth of the bills are hundreds, 1/4 of them are fifties, 1/10 of them are $20s. The rest of the bills
larisa [96]
If Simone has 20 bills, then:

1/5 of 20 = 4 [hundreds]
1/4 of 20 = 5 [fifites]
1/10 of 20 = 2 [$20s]

4 * 100 + 5 * 50 + 2 * 20 = 400 + 250 + 40 = 690 [out of $780]
4 + 5 + 2 = 11 [out of 20 bills]

So now we can easily find out she had 9 bills of tens - because 20 - 11 = 9 or because (780 - 690) ÷ 10 = 90 ÷ 10 = 9.
5 0
3 years ago
Describe at least two differences between constructing an inscribed regular hexagon and constructing an inscribed square.
liberstina [14]

Correct answer is A.

The diameter of the circle is used for the square construction, but the radius of the circle is used for the regular hexagon construction.

<h3>How to calculate the diameter?</h3>

If you know the radius of the circle, multiply by 2 to get the diameter. The radius is the distance from the center of the circle to the edge. For example, if the radius of a circle is 4 cm, then the diameter is 4 cm x 2 = 8 cm. If you know the circumference of the circle, divide by π to get the diameter.

<h3>Briefing:</h3>

The diameter of the circle is used for the square construction, but the radius of the circle is used for the regular hexagon construction which is A.

The diameter of the circle is used for the square as l=2r therefore corresponds to the diameter, while for a hexagon r=r being the radius of the circle.

To know more about Diameter visit:

brainly.com/question/5501950

#SPJ4

I understand that the question you are looking for is:

Describe at least two differences between constructing an inscribed regular hexagon and constructing an inscribed square.

A) The diameter of the circle is used for the square construction, but the radius of the circle is used for the regular hexagon construction.

B) The radius of the circle is used for the square construction, but the diameter of the circle is used for the regular hexagon construction.

C) The square will need two arcs along the circle, but the hexagon will need two arcs above and two arcs below the diameter of the circle.

D) The square will need six arcs along the circle, but the hexagon will need two arcs above and two arcs below the diameter of the circle.

7 0
1 year ago
5. Identify the correct trigonometry formula to use to solve for X.
Anna007 [38]

9514 1404 393

Answer:

  (a)  cos(55°) = 11/x

Step-by-step explanation:

The marked sides are the hypotenuse (x) and the side adjacent to the given angle (11). Then the relevant trig ratio is ...

  Cos = Adjacent/Hypotenuse

  cos(55°) = 11/x

4 0
2 years ago
Determine the arc length of the circle with radius 5.5 cm if it is subtended by a central angle of 5/2 radians round your answer
Advocard [28]

Answer:

yes

Step-by-step explanation:yesyesyesyesyesyesyesyesyes

3 0
3 years ago
Other questions:
  • A sphere and a cylinder have the same radius and height. The volume of the cylinder is 21 meters cubed. A sphere with height h a
    14·2 answers
  • Which value of jjj makes (5+3)j=48(5+3)j=48left parenthesis, 5, plus, 3, right parenthesis, j, equals, 48 a true statement? Choo
    13·1 answer
  • A $104,000 selling price with $24,000 down at 81⁄2% for 25 years results in a monthly payment of
    12·2 answers
  • Lucia and Marcus are playing a board game. They roll 2 dice (number cubes) to see who goes first. The person who rolls the highe
    5·1 answer
  • maria is using 208 ounces of water to make some soup. Her recipe calls for 2 fluid ounces of olive oil for every 13 cups of wate
    10·1 answer
  • -3a + 3 &gt; 33<br> +<br> -15 -14 -13 -12 -11 -10 9 -3
    6·1 answer
  • ? ahah i deleted this lol
    8·2 answers
  • Plot the vertex and the axis of symmetry of this function on a graph.<br><br> f(x) = (x + 2)2 − 6
    9·1 answer
  • How do you break it down when 350 goes in to 3500 how do you break it down to show how you got the answer
    9·1 answer
  • Help me with this! I'll give Brainliest!!!!!!!!!!!!!!!
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!