document.write( "Question 21661: I have an ellipse question, and I either have drawn a blank or there's a mistake somewhere. I know that I'm supposed to factor out where I can, but I just can't seem to make it work. I need to find the foci, vertex and center using the equation: 9x^2 + y^2 + 18x + 4y + 4 = 0. Can anyone help me???? \n" ); document.write( "
Algebra.Com's Answer #10449 by venugopalramana(3286)\"\" \"About 
You can put this solution on YOUR website!
9x^2 + y^2 + 18x + 4y + 4 = 0. STANDARD FORM FOR EQN.OF ELLIPSE IS
\n" ); document.write( "{(X-H)^2/A^2}+{(Y-K)^2/B^2}=1
\n" ); document.write( "LET US TRY TO PUT THE GIVEN EQN.IN THIS FORM
\n" ); document.write( "{9(X^2+2X+1-1)}+{Y^2+4Y+4-4}=-4
\n" ); document.write( "9(X+1)^2+(Y+2)^2=-4+4+9=9
\n" ); document.write( "DIVIDING WITH 9 THROUGH OUT WE GET
\n" ); document.write( "[(X+1)^2/1]+[(Y+2)^2/9]=1...THIS IS IN THE STANDARD FORM WITH
\n" ); document.write( "H=-1...K=-2.....A=1.....B=3.....SINCE WE HAVE A AS LESS THAN B WE GET
\n" ); document.write( "CENTRE =(H,K)=(-1,-2)
\n" ); document.write( "ECCENTRICITY =E =SQ.RT{(B^2-A^2)/B^2}=SQ.RT.{(9-1)/9}=2SQ.RT(2)/3
\n" ); document.write( "FOCI ARE GIVEN BY (H,K+BE) AND (H,K-BE)=(-1,-2+3*2SQ.RT2/3)
\n" ); document.write( "AND(-1,-2+3*2SQ.RT2/3)
\n" ); document.write( "THAT IS
\n" ); document.write( "=(-1,-2+2SQ.RT2)
\n" ); document.write( "AND(-1,-2+2SQ.RT2)
\n" ); document.write( "THERE IS NO VERTEX FOR ELLIPSE.\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
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