Given the hyperbola x2−y24=1x^2-\frac{y^2}{4}=1x2−4y2=1, find the length of the aaa-axis and bbb-axis.

a = 1 , b = 2 a=1,b=2 a = 1 , b = 2

Given the hyperbola x 2 − y 2 4 = 1 x^2-\frac{y^2}{4}=1 x 2 − 4 y 2 = 1 , find the length of the a a a -axis and b b b -axis.

Hey, everyone. Let's see if we can solve this problem. So here we have the hyperbola x squared minus y squared over four is equal to one, and we're asked to find the length of the a and b axis. So what I can do by looking at this problem is recognize that we have this form of a hyperbola. It's x squared over a squared minus y squared over b squared is equal to one. And by looking at the standard form of the hyperbola, I can see where things are going to line up. Now this a squared is going to correspond with what's in the denominator of this x squared. But notice that this x squared doesn't have a denominator, so we can just imagine that there's a one. So that means that a squared is equal to one. And what I can do is take the square root on both sides to get that a is one. So that's a. And for b squared, b squared is associated with this four. So we have the b squared is equal to four, and then if I take the square root on both sides, b is equal to the square root of four, which is two. So this is our a and b axis. And notice in this case that even though the b value was larger, it still doesn't become the a value. The a value is simply whatever comes first. And since this one came first, that's what we set a squared equal to, and that's how we got a. That's the answer. These are the a and b axes. Hope you found this helpful.