document.write( "Question 1086384: find the area bounded by the curve x^2=8y and its latus rectum \n" ); document.write( "

Algebra.Com's Answer #700627 by htmentor(1343) $\"\"$ $\"About$

You can put this solution on YOUR website!
The equation for a vertical parabola in terms of the vertex and focus is:
\n" ); document.write( "4p(y-k) = (x-h)^2, where (h,k) is the vertex and p is the distance from vertex to focus
\n" ); document.write( "In this case, the vertex is (0,0), and we can read off the value of p:
\n" ); document.write( "x^2 = 4py -> p = 2
\n" ); document.write( "So we need to find the area between the line y = 2 and the curve y = x^2/8
\n" ); document.write( "The area will be the difference of the functions integrated from -4 to 4,
\n" ); document.write( "since these are the endpoints where the two curves meet.
\n" ); document.write( "A =

\n" ); document.write( "A = 2*(2*4 - 64/24) = 32/3 \n" ); document.write( "

\n" );