Question

Find an equation in standard form for the hyperbola with vertices at (0, ±3) and foci at (0, ±7)

Answer 1

Answer:

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Step-by-step explanation:

Answer 2

The equation of a hyperbola is:

(x – h)^2 / a^2 - (y – k)^2 / b^2 = 1

 

So what we have to do is to look for the values of the variables:

For the given hyperbola : center (h, k) = (0, 0)
a = 3(distance from center to vertices)
a^2 = 9

c = 7 (distance from center to vertices; given from the foci)
c^2 = 49

 

By the hypotenuse formula:
c^2 = a^2 + b^2
b^2 = c^2 - a^2

b^2 =  49 – 9

b^2  = 40

Therefore the equation of the hyperbola is:

(x^2 / 9) – (y^2 / 40) = 1