Standard equation of Ellipse

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Write the equation of the *ellipse* in standard from $$25x^{2}+4y^{2}-150x+56y+321 = 0 $$

**Answer**

$25x^{2}+4y^{2}-150x+56y+321 = 0 $

$25x^{2}-150x+4y^{2}+56y=-321$

$25(x^{2}-6x)+4(y^{2}+14y)=-321$

$25(x^{2}-6x+9)+4(y^{2}+14y+49)=-321+225+196$

$25(x-3)^2+4(y+7)^2 = 100$

$\frac{1}{4}(x-3)^2+\frac{1}{25}(y+7)^2 = 1$

$\frac{(x-3)^2}{{2}^2}+\frac{(y+7)^2}{{5}^2} = 1$