Standard equation of Ellipse

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Write the equation of the *ellipse* in standard from $$36x^{2}+49y^{2}-216x+294y-999 = 0 $$

**Answer**

$36x^{2}+49y^{2}-216x+294y-999 = 0 $

$36x^{2}-216x+49y^{2}+294y=999$

$36(x^{2}-6x)+49(y^{2}+6y)=999$

$36(x^{2}-6x+9)+49(y^{2}+6y+9)=999+324+441$

$36(x-3)^2+49(y+3)^2 = 1764$

$\frac{1}{49}(x-3)^2+\frac{1}{36}(y+3)^2 = 1$

$\frac{(x-3)^2}{{7}^2}+\frac{(y+3)^2}{{6}^2} = 1$