document.write( "Question 787615: Find the center and the foci of the ellipse
\n" ); document.write( "5x^2+12y^2-30x+24y+7=0 \n" ); document.write( "

Algebra.Com's Answer #478247 by lwsshak3(11628) $\"\"$ $\"About$

You can put this solution on YOUR website!
Find the center and the foci of the ellipse
\n" ); document.write( "5x^2+12y^2-30x+24y+7=0
\n" ); document.write( "5x^2-30x+12y^2+24y=-7
\n" ); document.write( "complete the square
\n" ); document.write( "5(x^2-6x+9)+12(y^2+2y+1)=-7+45+12
\n" ); document.write( "5(x-3)^2+12(y+1)^2=50
\n" ); document.write( "divide by 50
\n" ); document.write( "(x-3)^2/10+12(y+1)^2/(50/12)=1
\n" ); document.write( "(x-3)^2/10+12(y+1)^2/(25/6)=1
\n" ); document.write( "This is an equation of an ellipse with horizontal major axis
\n" ); document.write( "Its standard form: $\"%28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1\"$ , a>b, (h,k)=(x,y) coordinates of center.
\n" ); document.write( "..
\n" ); document.write( "For given ellipse:
\n" ); document.write( "center: (3,-1)
\n" ); document.write( "a^2=10
\n" ); document.write( "b^2=25/6
\n" ); document.write( "c^2=a^2-b^2=10-25/6=35/6
\n" ); document.write( "c=√(35/6)≈2.42
\n" ); document.write( "foci:(3ąc,-1)=(3ą2.42,-1)=(0.58,-1) and (5.42,-1)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );