Standard equation of Ellipse

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Write the equation of the *ellipse* in standard from $$36x^{2}+25y^{2}+504x+100y+964 = 0 $$

**Answer**

$36x^{2}+25y^{2}+504x+100y+964 = 0 $

$36x^{2}+504x+25y^{2}+100y=-964$

$36(x^{2}+14x)+25(y^{2}+4y)=-964$

$36(x^{2}+14x+49)+25(y^{2}+4y+4)=-964+1764+100$

$36(x+7)^2+25(y+2)^2 = 900$

$\frac{1}{25}(x+7)^2+\frac{1}{36}(y+2)^2 = 1$

$\frac{(x+7)^2}{{5}^2}+\frac{(y+2)^2}{{6}^2} = 1$