Question 949353
Major axis: The longest diameter of an ellipse.
Minor axis: The shortest diameter of an ellipse. 

recall:
{{{x^2/a^2 + y^2/b^2 = 1}}}....the horizontal major axis
{{{x^2/b^2 + y^2/a^2 = 1}}}....the vertical major axis


1. 
{{{64x^2 + 25y^2 = 6400}}}...first write it in {{{x^2/a^2 + y^2/b^2 = 1}}} form

{{{64x^2/6400 + 25y^2/ 6400= 6400/6400}}}

{{{x^2/100 + y^2/256= 1}}} =>here we have the vertical major axis and the {{{a^2}}} lies under {{{y}}} and {{{b^2}}} under {{{x}}}

{{{b^2=100}}} => {{{b=10}}}
{{{a^2=256}}} => {{{a=16}}}
so,
the major axis has length: => {{{a=16}}}
the minor axis has length: => {{{b=10}}}

 
{{{ graph( 600, 600, -35, 35, -35, 35, sqrt((1-x^2/100)256), -sqrt((1-x^2/100)256)) }}} 


2.

{{{x^2/(100) + y^2/(49) = 1}}}  =>here we have the horizontal major axis and the {{{a^2}}} lies under {{{x}}} and {{{b^2}}} under {{{y}}} 

{{{a^2=100}}} => {{{a=10}}}
{{{b^2=49}}} => {{{b=7}}}

Length of major axis is: {{{a =10}}}
Length of minor axis is: {{{b =7}}}

{{{ graph( 600, 600, -15, 15, -15, 15, sqrt((1-x^2/100)49), -sqrt((1-x^2/100)49)) }}}