Question

Which is the standard equation of the hyperbola centered at the origin, with a vertical transverse axis and values of a = 8 and b = 9?

A) x squared over 64 minus y squared over 81 equals 1
B) x squared over 81 minus y squared over 64 equals 1
C) y squared over 64 minus x squared over 81 equals 1
D) y squared over 81 minus x squared over 64 equals 1

Answer 1

The standard equation of a hyperbola centered at the origin with a vertical transverse axis is x^2/a^2 - y^2/b^2 = 1, where a and b are the semi-major and semi-minor axes. Substituting the given values of a = 8 and b = 9, we find that the correct equation is x^2/64 - y^2/81 = 1.

So, the correct answer is option A) x2/64 - y2/81 = 1.

Step-by-step explanation:

The standard equation of a hyperbola centered at the origin, with a vertical transverse axis, is given by:

x2/a2 - y2/b2 = 1

Given that a = 8 and b = 9, we can substitute these values into the equation:

x2/82 - y2/92 = 1

Simplifying, we get:

x2/64 - y2/81 = 1

Therefore, the correct answer is option A) x2/64 - y2/81 = 1.