SOLUTION: Write x^2+25y^2+6x-100y+9=0 in standard form. Find conic and center

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Question 795185: Write x^2+25y^2+6x-100y+9=0 in standard form. Find conic and center

Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Complete The Square for the x and for the y, and then simplify into whichever standard for will be suitable to the type of conic section.

x%5E2%2B25y%5E2%2B6x-100y%2B9=0
x%5E2%2B6x%2B25y%5E2-100y%2B9=0
%28x%5E2%2B6x%29%2B+25%28y%5E2-4y%29%2B9=0
And continuing without explanation for this step section,
%28x%5E2%2B6x%2B9%29%2B25%28y%5E2-4y%2B4%29%2B9=9%2B25%2A4
%28x%2B3%29%5E2%2B25%28y-2%29%5E2=100
The squares are now completed.
%281%2F100%29%28%28x%2B3%29%5E2%2B25%28y-2%29%5E2%29=100%2F100
highlight%28%28x%2B3%29%5E2%2F10%5E2%2B%28y-2%29%5E2%2F2%5E2=1%29

Compare that to standard form of an ellipse: %28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1,
where a is the distance from either vertex to the center along the x axis, b is the distance from either vertical vertex to the center along the y axis; if assuming center were on the origin --- although for YOUR example, center is NOT...
Standard Form for ellipse conventionally uses a for the longer axis and b for the shorter axis.
and the center point is (h,k).

The center point for your example is (-3, 2).