Math problem about hyperbolas?

Question

In a equation for a hyperbola, you know how you have a^2 and b^2 as denominators. How do I know where the bigger number and smaller number go to replace a^2 and b^2. What I am trying to say is.... In an equation for a hyperbola, how do I know if I should replace a^2 with the bigger number or the smaller number?

Sources needed....

Answer 1

i dont think that it really matters....in the equation for a hyperbola, you add both the (x+h)^2 and the (y+k)^2, so i dont think that it really matters what side it is on

Answer 2

As i am looking at my pre-cal book determining how to answer you question, I came up with a solution.

Usually, the smaller number is always "a", and a is what determines the vertices of the hyperbola. If it is a horizontal hyperbola, the x^2 would be above the a^2. If it is vertical, the y^2 would be above the a^2. The equations for the hyperbola are as follows:

x^2/a^2-y^2/b^2=1 if it is horizontal

y^2/a^2-x^2/b^2=1 if it is vertical.

The only way that a or b would matter in dertermining them is only in the ellipse, where the bigger number is always a. In hyperbolas, it doesn't matter. Hope this helps you out, and if you have anymore questions, email me at [e-mail] and I will answer any questions you may have.

Answer 3

Don't confuse the a² and b² of the hyperbola with the a² and b² of the ellipse. For the hyperbola the a² could be larger, smaller, or the same as the b². The a² is determined by which way the hyperbolas open.

If the hyperbolas are horizontal the equation is:

(x - h)²/a² + (y - k)²/b² = 1

If the hyperbolas are vertical the equation is:

(y - k)²/a² + (x - h)²/b² = 1

Answer 4

sorry i have an exam on sunday MATHS EXAM
and i totally forget wat hyperbolas are actually
i apologize for tht