Algebra II

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Hyperbolas:
Could someone please tell me how to determine if the following indicate the foci are on the x-axis or the y-axis?
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

  • Algebra II -

    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.

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