document.write( "Question 650104: What is the solution of hyperbola 2x^2+2y^2-8x+12y+2=0? \n" ); document.write( "
Algebra.Com's Answer #407188 by ewatrrr(24785)\"\" \"About 
You can put this solution on YOUR website!
 
\n" ); document.write( "Hi,
\n" ); document.write( "2x^2+2y^2-8x+12y+2=0
\n" ); document.write( "2(x-2)^2 + 2(y+3)^2 = -2 + 8 + 18
\n" ); document.write( "\"%28x-2%29%5E2+%2B+%28y%2B3%29%5E2+=+12\"
\n" ); document.write( "See below descriptions of various conics
\n" ); document.write( "Standard Form of an Equation of a Circle is \"%28x-h%29%5E2+%2B+%28y-k%29%5E2+=+r%5E2\"
\n" ); document.write( "where Pt(h,k) is the center and r is the radius\r
\n" ); document.write( "\n" ); document.write( " Standard Form of an Equation of an Ellipse is \"%28x-h%29%5E2%2Fa%5E2+%2B+%28y-k%29%5E2%2Fb%5E2+=+1+\"
\n" ); document.write( "where Pt(h,k) is the center. (a variable positioned to correspond with major axis)
\n" ); document.write( " a and b are the respective vertices distances from center
\n" ); document.write( " and ±\"sqrt%28a%5E2-b%5E2%29\"are the foci distances from center: a > b\r
\n" ); document.write( "\n" ); document.write( "Standard Form of an Equation of an Hyperbola opening up and down is:
\n" ); document.write( " \"%28y-k%29%5E2%2Fb%5E2+-+%28x-h%29%5E2%2Fa%5E2+=+1\" with C(h,k) and vertices 'b' units up and down from center, 2b the length of the transverse axis
\n" ); document.write( "Foci \"sqrt%28a%5E2%2Bb%5E2%29\"units units up and down from center, along x = h
\n" ); document.write( "& Asymptotes Lines passing thru C(h,k), with slopes m = ± b/a\r
\n" ); document.write( "\n" ); document.write( "Standard Form of an Equation of an Hyperbola opening right and left is:
\n" ); document.write( " \"%28x-h%29%5E2%2Fa%5E2+-+%28y-k%29%5E2%2Fb%5E2+=+1\" with C(h,k) and vertices 'a' units right and left of center, 2a the length of the transverse axis
\n" ); document.write( "Foci are \"sqrt%28a%5E2%2Bb%5E2%29\" units right and left of center along y = k
\n" ); document.write( "& Asymptotes Lines passing thru C(h,k), with slopes m = ± b/a \r
\n" ); document.write( "\n" ); document.write( "the vertex form of a Parabola opening up(a>0) or down(a<0), \"y=a%28x-h%29%5E2+%2Bk\"
\n" ); document.write( "where(h,k) is the vertex and x = h is the Line of Symmetry
\n" ); document.write( "The standard form is \"%28x+-h%29%5E2+=+4p%28y+-k%29\", where the focus is (h,k + p)
\n" ); document.write( "and length of the latus rectum is 4p.\r
\n" ); document.write( "\n" ); document.write( "the vertex form of a Parabola opening right(a>0) or left(a<0), \"x=a%28y-k%29%5E2+%2Bh\"
\n" ); document.write( " where(h,k) is the vertex and y = k is the Line of Symmetry
\n" ); document.write( "The standard form is \"%28y+-k%29%5E2+=+4p%28x+-h%29\", where the focus is (h +p,k )
\n" ); document.write( "and length of the latus rectum is 4p.
\n" ); document.write( " \n" ); document.write( "
\n" );