Standard equation of Ellipse

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Write the equation of the *ellipse* in standard from $$16x^{2}+9y^{2}-224x+54y+289 = 0 $$

**Answer**

$16x^{2}+9y^{2}-224x+54y+289 = 0 $

$16x^{2}-224x+9y^{2}+54y=-289$

$16(x^{2}-14x)+9(y^{2}+6y)=-289$

$16(x^{2}-14x+49)+9(y^{2}+6y+9)=-289+784+81$

$16(x-7)^2+9(y+3)^2 = 576$

$\frac{1}{36}(x-7)^2+\frac{1}{64}(y+3)^2 = 1$

$\frac{(x-7)^2}{{6}^2}+\frac{(y+3)^2}{{8}^2} = 1$