Standard equation of Ellipse

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Write the equation of the *ellipse* in standard from $$9x^{2}+y^{2}-108x-8y+259 = 0 $$

**Answer**

$9x^{2}+y^{2}-108x-8y+259 = 0 $

$9x^{2}-108x+y^{2}-8y=-259$

$9(x^{2}-12x)+(y^{2}-8y)=-259$

$9(x^{2}-12x+36)+(y^{2}-8y+16)=-259+324+16$

$9(x-6)^2+(y-4)^2 = 81$

$\frac{1}{9}(x-6)^2+\frac{1}{81}(y-4)^2 = 1$

$\frac{(x-6)^2}{{3}^2}+\frac{(y-4)^2}{{9}^2} = 1$