document.write( "Question 857860: Find the vertices and foci of the ellipse given by the equaiton 9x^2 + 4y^2 + 36x -8y +4 +0 \n" ); document.write( "

Algebra.Com's Answer #516954 by lwsshak3(11628) $\"\"$ $\"About$

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Find the vertices and foci of the ellipse given by the equaiton
\n" ); document.write( "9x^2 + 4y^2 + 36x -8y +4 +0
\n" ); document.write( "9x^2+36x+4y^2-8y=-4
\n" ); document.write( "complete the square:
\n" ); document.write( "9(x^2+4x+4)+4(y^2-2y+1)=-4+36+4
\n" ); document.write( "9(x+2)^2+4(y-1)^2=36
\n" ); document.write( " $\"%28x%2B2%29%5E2%2F4%2B%28y-1%29%5E2%2F9=1\"$
\n" ); document.write( "This is an equation of an ellipse with vertical major axis.
\n" ); document.write( "Its standard form of equation: $\"%28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%5E2%2Fa%5E2=1\"$ , a>b, (h,k)=(x,y) coordinates of center
\n" ); document.write( "center: (-2,1)
\n" ); document.write( "a^2=9
\n" ); document.write( "a=3
\n" ); document.write( "vertices: (-2, 1ąa)=(-2,1ą2)=(-2,-1) and (-2,3)
\n" ); document.write( "b^2=4
\n" ); document.write( "b=2
\n" ); document.write( "c^2=a^2-b^2=9-4=5
\n" ); document.write( "c=√5≈2.2
\n" ); document.write( "foci: (-2, 1ąc)=(-2,1ą2.2)=(-2,-1.2) and (-2,3.2)
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