Question

Which hyperbola has both vertices in the same quadrant?

Answer 1

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