Question 818717
x = 5 sin t,    y = 6 cos t
Solve the first equation for sin(t):
{{{x/5 = sin(t)}}}
and the second equation for cos(t):
{{{y/6 = cos(t)}}}
Square both sides of both equations:
{{{(x/5)^2 = sin^2(t)}}} , {{{(y/6)^2 = cos^2(t)}}}
{{{x^2/25 = sin^2(t)}}} , {{{y^2/36 = cos^2(t)}}}
Add the two equations together:
{{{x^2/25 + y^2/36 = sin^2(t) + cos^2(t)}}}
You might see now why we've done what we've done. The right side should be recognized as a 1:
{{{x^2/25 + y^2/36 = 1}}}