Question

What is the transverse axis and conjugate axis of the hyperbola x-squared over 225 minus y–squared over 144 equals 1?

Answer 1

\[\frac{ x ^{2} }{ 225 }-\frac{ y^{2} }{ 144 } = 1\]

Answer 2

\[\frac{x^2}{225} - \frac{y^2}{144} = 1\]

Standard form is \[\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\]Do you recall the meanings of \(a\) and \(b\)?

Answer 3

No, but would that make a=15 and b=12?

Answer 4

@whpalmer4

Answer 5

yes, those are the correct values of \(a\) and \(b\).

Answer 6

What else do I need to know?

Answer 7

well, we need to figure out the transverse and conjugate axes.

Answer 8

How do you do that?

Answer 9

well, it turns out that \(a\) and \(b\) are 1/2 of the lengths of those axes, assuming I'm remembering correctly :-)

Answer 10

So I multiply them by 2 to get 24 and 30?

Answer 11

But which is the transverse and conjugate?

Answer 12

The transverse axis is the one that connects the vertices of the hyperbola. It has length 2a. The conjugate axis is the one at right angles to that, and has length 2b.

Answer 13

Thank you!