document.write( "Question 1144228: Determine the general equation of the ellipse with center (0,0), a focus of (0, √7), and a vertex of (0,4). \n" ); document.write( "

Algebra.Com's Answer #765278 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The center is at (0,0), and the coordinates of the vertex and focus tell us the major axis is vertical. The general equation is then

\n" ); document.write( " $\"x%5E2%2Fb%5E2%2By%5E2%2Fa%5E2+=+1\"$ [1]

\n" ); document.write( "where a is the semi-major axis and b is the semi-minor axis.

\n" ); document.write( "The distance from the center to each focus is c, where a, b, and c are related by

\n" ); document.write( " $\"c%5E2+=+a%5E2%2Bb%5E2\"$ [2]

\n" ); document.write( "The given coordinates of a focus and a vertex tell us c = sqrt(7) and a = 4.

\n" ); document.write( "Use those values in [2] to determine the value of a; then write the equation [1] using the values of a and b. \n" ); document.write( "

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