We're just learning about ellipses and conics, and I'm a bit confused with ellipses, parabolas, circles, and hyperbolas, so a little help with this sample problem would be great.

In which of the following equations would the ellipse have foci on the y-axis, the x-axis, or neither?


Graph for the first equation


Graph for the second equation

I tried graphing these already, but I'm still not exactly sure where the foci lies. In fact, what does each number in the equation of an ellipse represent? I apologize for the very ignorant questions, but we just started learning about conics. :)

  • $\begingroup$ One may speak of where a focus lies, or of where the two foci lie, but not of "where the foci lies". "Foci" is the plural of "focus". ${}\qquad{}$ $\endgroup$ – Michael Hardy Dec 23 '14 at 21:20
  • $\begingroup$ I apologize for the misuse of words. Thank you for the correction. $\endgroup$ – user202767 Dec 23 '14 at 21:21

You don't need to know the exact location of the foci in order to know what line they are on. They are always on the major axis.

  • $\begingroup$ So would the two foci lie on the y-axis? $\endgroup$ – user202767 Dec 23 '14 at 21:24
  • $\begingroup$ In the first case above they're on the $y$-axis; in the second on the $x$-axis. ${}\qquad{}$ $\endgroup$ – Michael Hardy Dec 23 '14 at 21:25

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