Sketch the graph of 4x^2 + 9y^2 = 144. Is this an ellipse?

[kasse]

I'm going to sketch the graph of the eq. 4x^2 + 9y^2 = 144

This is an ellipse with its center at the origo and major semiaxis 6 and minor semiaxis 4. But how do I find the foci?

 

[tim_lou]

a^2=b^2+c^2
where c is the focal length.

the equation comes directly from one definition of ellipse:
the sum of distance between any point on the ellipse and the foci = 2a.

 

[kasse]

Ah, makes sense. Thank you!