document.write( "Question 439456: Find the vertices and foci of the conic. 25x^2 + 4y^2 + 50x = 75 \n" ); document.write( "

Algebra.Com's Answer #303705 by Gogonati(855) $\"\"$ $\"About$

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We rewrite the equation in the form: $\"25x%5E2%2B50x%2B25%2B4y%5E2=75%2B25\"$ simplify:\r
\n" ); document.write( "\n" ); document.write( " $\"25%28x%2B1%29%5E2%2B4y%5E2=100\"$ , divide both sides by 100 and have:\r
\n" ); document.write( "\n" ); document.write( " $\"%28x%2B1%29%5E2%2F4%2By%5E2%2F25=1\"$ , which is the equation of ellipse centered at (-1, 0).\r
\n" ); document.write( "\n" ); document.write( "the vertices are:(-1, 5) and (-1, -5).\r
\n" ); document.write( "\n" ); document.write( "The foci are: $\"c%5E2=b%5E2-a%5E2\"$ => $\"c%5E2=25-4\"$ => c=+/-sqrt(21) and the foci:\r
\n" ); document.write( "\n" ); document.write( "(-1, $\"sqrt%2821%29\"$ ) and (-1,- $\"sqrt%2821%29\"$ ).\r
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