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Phantasy [73]
3 years ago
8

Which hyperbola has both vertices in the same quadrant?

Mathematics
1 answer:
Serggg [28]3 years ago
4 0

Answer:

Given a hyperbola with an equation:

Foci will have coordinates:

F₁ (xc - c, yc) and F₂ (xc - c, yc)

where c = √(a² + b²)

While given a hyperbola with an equation:

Foci will have coordinates:

F₁ (xc , yc - c) and F₂ (xc , yc - c)

where c = √(b² + a²)

Now, start looking at the equations you are given as a solution and note the option A and C do not represent a hyperbola since they don't have both parenthesis squared.

For option B) you have:

xc = 24

yc = 1

a² = 24² = 576

b² = 7² = 49

Therefore:

c = √(576+49) = √625 = 25

and

F₁(-1 , 1)  F₂(49 , 1)

which are not on the same quadrant.

For option D) you have:

yc = 16

xc = -1

a² = 9² = 81

b² = 12² = 144

Therefore:

c = √(144+81) = √225 = 15

and

F₁(-1 , 1)  F₂(-1 , 31)

which are on the same quadrant.

Hence, the correct answer is b i think

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Answer:

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Step-by-step explanation:

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nirvana33 [79]

Step-by-step explanation:

The quadratic equation is x² + (p - 5)x + 2q = 0.

By Vieta's Formula,

we have SOR = -b/a and POR = c/a.

=> (-3) + (6) = -(p - 5) and (-3)(6) = 2q.

=> 3 = 5 - p and -18 = 2q

Hence, p = 2 and q = -9.

Alternate Method:

We have (x + 3) and (x - 6) as factors of the quadratic equation x² + (p - 5)x + 2q = 0.

=> (x + 3)(x - 6) = x² - 3x - 18.

By Comparing Coefficients,

(p - 5) = -3 and 2q = 18.

Hence p = 2 and q = -9.

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Write the equation in standard form of the line that has x-intercept 7 and y-intercept 4.
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