Finding the vertices of an Ellipse

Question

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?

Answer 1

Because the ellipse is centered at the origin, the verticies occur where one of the coordinates equals 0.

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 $(0,{\sqrt{251} \over 7})$.