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given: (x+6)^2/4+(y-5)^2/16=1
\n" ); document.write( "standard form of an ellipse, (x-h)^2/b^2+(y-K)^2/a^2,a>b
\n" ); document.write( "let me first describe what the ellipse looks like just from inspection of the expression
\n" ); document.write( "this is an ellipse elongated (major axis) in the vertical direction because the y-term has the larger denominator (a).
\n" ); document.write( "coordinates of the center are (-6,5)
\n" ); document.write( "a^2=16
\n" ); document.write( "a=4
\n" ); document.write( "b^2=4
\n" ); document.write( "b=2
\n" ); document.write( "here is how to solve for y\r
\n" ); document.write( "\n" ); document.write( "multiply given expression by 16
\n" ); document.write( "4(x+6)^2+(y-5)^2=16
\n" ); document.write( "(y-5)^2=16-4(x+6)^2
\n" ); document.write( "take the sqrt of both sides
\n" ); document.write( "y-5 =sqrt(16-4(x+6)^2)
\n" ); document.write( "y=5ħsqrt(16-4(x+6)^2)\r
\n" ); document.write( "\n" ); document.write( "here is how to check to see if this is correct\r
\n" ); document.write( "\n" ); document.write( "let x=-6, the x coordinate of the center
\n" ); document.write( "y=5ħsqrt(16-4(-6+6)^2)=5ħsqrt(16)
\n" ); document.write( "y=5ħ4=9 and 1, which are the y coordinates of the vertices of the given ellipse.\r
\n" ); document.write( "\n" ); document.write( "another point we could check is when x=-4
\n" ); document.write( "y=5ħsqrt((16-4(-4+6)^2)=5ħsqrt(16-16)=5(the y coordinate of minor axis on the right side\r
\n" ); document.write( "\n" ); document.write( "ans: the formula to use in isolating y in given ellipse is: y=5ħsqrt(16-4(x+6)^2) \n" ); document.write( "