Algebra II
posted by Jed on .
Hyperbolas:
Could someone please tell me how to determine if the following indicate the foci are on the xaxis or the yaxis?
x^2/4 y^2/16 = 1
x^2/49  y^2/9 = 1
x^2/36  y^2/16 = 1
please explain how to set the equations up
thank you

These are all hyperbolas.
Look at wwhat happens when y = 0 (on the x axis) and when x = 0 (on the y axis)
In all cases, when y = 0, there are two real solutions for x. In the first one for example when y = 0, x = 2 or x = 2
However when x = 0, there is no real solution for y. In other words the hyperbolas never reach the y axis and open left and right. All foci are therefore located on the x axis.