Question

[
frac{x^{2}}{4}+frac{y^{2}}{9}=1
]
since the denominator of ( frac{y^{2}}{9} ) is larger than the denominator of ( frac{x^{2}}{4} ). the major axis is along the ( y ) -axis. Comparing the given equation with the standard equation ( frac{x^{2}}{b^{2}}+frac{y^{2}}{a^{2}}=1, ) we have ( b=2 ) and ( a=3 )
( mathrm{Also} )
[
c=sqrt{a^{2}-b^{2}}=sqrt{9-4}=sqrt{5}
]
and
[
e=frac{c}{a}=frac{sqrt{5}}{3}
]
Hence the foci are ( (0, sqrt{5}) ) and ( (0,-sqrt{5}), ) vertices are (0,3) and ( (0,-3), ) length of the
major axis is 6 units, the length of the minor axis is 4 units and the eccentricity of the
ellipse is ( frac{sqrt{5}}{3} )

# Example 10 Find the coordinates of the foci, the vertices, the lengths of major and minor axes and the eccentricity of the ellipse 9x? + 4v2 = 36.

Solution