document.write( "Question 818717: Find an equation in x and y whose graph contains the points on the curve C.
\n" ); document.write( "x = 5 sin t, y = 6 cos t; 0 ≤ t ≤ 2π \n" ); document.write( "

Algebra.Com's Answer #492821 by jsmallt9(3758) $\"\"$ $\"About$

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x = 5 sin t, y = 6 cos t
\n" ); document.write( "Solve the first equation for sin(t):
\n" ); document.write( " $\"x%2F5+=+sin%28t%29\"$
\n" ); document.write( "and the second equation for cos(t):
\n" ); document.write( " $\"y%2F6+=+cos%28t%29\"$
\n" ); document.write( "Square both sides of both equations:
\n" ); document.write( " $\"%28x%2F5%29%5E2+=+sin%5E2%28t%29\"$ , $\"%28y%2F6%29%5E2+=+cos%5E2%28t%29\"$
\n" ); document.write( " $\"x%5E2%2F25+=+sin%5E2%28t%29\"$ , $\"y%5E2%2F36+=+cos%5E2%28t%29\"$
\n" ); document.write( "Add the two equations together:
\n" ); document.write( " $\"x%5E2%2F25+%2B+y%5E2%2F36+=+sin%5E2%28t%29+%2B+cos%5E2%28t%29\"$
\n" ); document.write( "You might see now why we've done what we've done. The right side should be recognized as a 1:
\n" ); document.write( " $\"x%5E2%2F25+%2B+y%5E2%2F36+=+1\"$
\n" ); document.write( " \n" ); document.write( "

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