Question 217058
You can start with a graph of the inequality {{{x^2+4y^2 < 64}}} to get you started: 

{{{graph( 500, 500, -10, 10, -10, 10, x^2+4y^2 < 64 )}}}

This site has a general graphing calculator that plots inequalities. 

You can set x = 0 and find out where the ellipse cross the Y axis, by solving for Y: {{{0^2 + 4y^2 = 64}}}, which is easy ({{{y=+-4}}}). Then do the same to find out where it crosses the X axis with Y=0: {{{x^2 + 4*0^2 = 64}}} ({{{x=+-8}}}).