25x2 + 225y2 = 900

Question

Graph the equation

25x2 + 225y2 = 900. Identify the vertices, co-vertices, and foci of the ellipse.

 

Answer 1

This can be written:

x²/36+y²/4=1 so a=6 and b=2 (lengths of semi-major and semi-minor axes).

Eccentricity e=√(1-(b/a)²)=√(1-1/9)=√(8/9)=(2√2)/3.

Foci are (±ae,0)=(-4√2,0) and (4√2,0).

Vertices are (-6,0) and (6,0) and co-vertices are (0,-2) and (0,2).