Question

What is the equation for the hyperbola shown?
x^2/8^2-y^2/5^2 = 1
x^2/5^2-y^2/8^2 = 1
y^2/8^2-x^2/5^2 = 1
y^2/5^2-x^2/8^2 = 1
Answer is D !!!!!! welcome guys

Answer 1

Answer: d, its the only one that is possible

Step-by-step explanation:

Answer 2

The equation of the hyperbola is y^2/5^2 - x^2/8^2 =1

How to determine the equation of the hyperbola?

The equation of a hyperbola is represented as;

(y - k)^2/b^2 - (x-h)^2/a^2 =1

From the complete question, we have:

Center (h,k) = (0,0)

So, we have:

(y - 0)^2/b^2 - (x - 0)^2/a^2 =1

y^2/b^2 - x^2/a^2 =1

The distance between the center and the vertex is:

a = 8

The distance between the center and the foci is:

c = sqrt(89)

Calculate b using the following equation

b^2 = c^2 - a^2

This gives

b^2 = 89 - 8^2

b^2 = 89 - 64

b^2 = 25

Express as squares

b^2 = 5^2

So, we have:

y^2/5^2 - x^2/8^2 =1

Hence, the equation of the hyperbola is y^2/5^2 - x^2/8^2 =1

Read more about hyperbolas at:

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