Given equation of ellipse
#49x^2+144y^2-196x-720y-668=0#
#49(x^2-4x+4)+144(y^2-5y+25/4)-196-900-668=0#
#49(x-2)^2+144(y-5/2)^2=1764#
#\frac{(x-2)^2}{36}+\frac{(y-5/2)^2}{49/4}=1#
#\frac{(x-2)^2}{6^2}+\frac{(y-5/2)^2}{(7/2)^2}=1#
Comparing above equation with the standard form of ellipse
#X^2/a^2+Y^2/b^2=1# we get
#X=x-2, Y=y-5/2, a=6, b=7/2#
Eccentricity of ellipse
#e=\sqrt{1-b^2/a^2}=\sqrt{1-\frac{49/4}{36}}=\sqrt{95}/{12}#
Center of ellipse
#X=0, Y=0#
#x-2=0, y-5/2=0#
#(2, 5/2)#
Vertices of Ellipse
#(X=\pm a, Y=0) \ & \ (X=0, Y=\pm b)#
#(x-2=\pm6, y-5/2=0)\ &\ (x-2=0, y-5/2=\pm7/2)#
#(2\pm6, 5/2)\ &\ (2, 5/2\pm7/2)#
Focii of ellipse
#(X=\pmae, Y=0)#
#(x-2=\pm\sqrt{95}/2, y-5/2=0)#
#(2\pm\sqrt{95}/2, 5/2)#
Latus rectum of ellipse
#\frac{2b^2}{a}=\frac{2(49/4)}{6}=49/12#
