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You can put this solution on YOUR website!
Find the formula.
\n" ); document.write( "Ellipse with foci at (5, 1) and (-1, 1) and contains a point at (1, 3)
\n" ); document.write( "**
\n" ); document.write( "Gleaned from coordinates of foci, this is an ellipse with a horizontal major axis (x changes, but y does not change) of the standard form: (x-h)^2/a^2+(y-k)^2/b^2=1, a>b, with (h,k) being the (x,y) coordinates of the center.
\n" ); document.write( "For given equation:
\n" ); document.write( "center: (2,1)
\n" ); document.write( "Equation: (x-2)^2/a^2+(y-1)^2/b^2=1
\n" ); document.write( "From foci info, c=3
\n" ); document.write( "c^2=a^2-b^2=9
\n" ); document.write( "b^2=a^2-9
\n" ); document.write( "using (x,y) coordinates of given point (1, 3) to solve for a
\n" ); document.write( "(x-2)^2/a^2+(y-1)^2/b^2=1
\n" ); document.write( "(1-2)^2/a^2+(3-1)^2/(a^2-9)=1
\n" ); document.write( "1/a^2+4/(a^2-9)=1
\n" ); document.write( "a^2-9+4a^2=a^4-9a^2
\n" ); document.write( "a^4-9a^2-a^2-4a^2+9
\n" ); document.write( "a^4-14a^2+9=0
\n" ); document.write( "solving a with quadratic formula: (let student do this)
\n" ); document.write( "a^2=13.3246
\n" ); document.write( "b^2=a^2-9=4.3246
\n" ); document.write( "..
\n" ); document.write( "equation:
\n" ); document.write( "(x-2)^2/13.3246+(y-1)^2/4.3246=1\r
\n" ); document.write( "\n" ); document.write( "comment: I was hoping to get an exact answer but this is the closest I could get. The answer itself, however, is not as important as the method to get the answer.
\n" ); document.write( "See the graph below as a visual check on the answer.
\n" ); document.write( "y=±(4.3256-(4.3256/13.3246)(x-2)^2)^.5+1
\n" ); document.write( "