# Finding the vertices of an Ellipse

Trying to find the vertices of a ellipse.

This is what I got

And so used WolframAlpha just to test it out, this is my third time using it. This is the solution that I got

So as you can see in the implicit plot it shows that in the positive y-axis it is 2.26? would be the answer?

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What is your definition of "vertex" in this context? The ones I can find on the net all imply that the vertices of this ellipse would be its intersection with the $x$ axis. The intersections with the $y$ axis would be "co-vertices". –  Henning Makholm Oct 21 '12 at 14:27
I guess the vertices in this case will be the points of the ellipse in the graph –  JackyBoi Oct 21 '12 at 14:42

Setting $x=0$: $$49y^2=251$$ $$y = \pm {\sqrt{251} \over 7}$$
Setting $y=0$: $$23x^2 = 251$$ $$x = \pm \sqrt{251 \over 23}$$
Your question asks for the positive x intercept($y=0$). That's $(0,{\sqrt{251} \over 7})$.