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Nataly_w [17]
2 years ago
7

Your Turn!

Mathematics
1 answer:
Pachacha [2.7K]2 years ago
5 0
B don’t quote me if I’m wrong
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Select the correct answer. which hyperbola has both foci lying in the same quadrant? a. b. c. d.
faltersainse [42]

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.

7 0
2 years ago
What is 12.346 as a fraction? <br> Please help
Brilliant_brown [7]
Answer: 6173/500 HOPE IT HELPED!
6 0
3 years ago
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Can someone please tell me how to solve this?
beks73 [17]

Because this is an expression, you cannot solve for a value of x.

3x + 96

We can factor a 3 out of this to simplify it further.

3(x + 32) is the simplified form of the given expression.

5 0
3 years ago
Problem #2 - 8.2B
Bond [772]
Answer J

if you simplify 98 it’ll give you 9.89...
5 0
2 years ago
What is 4+3-1x22 plz help
cricket20 [7]
4+3-1x22 
4+3-22
7-22 
-15 
So -15 is the answer
5 0
3 years ago
Read 2 more answers
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