Standard equation of Ellipse

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Write the equation of the *ellipse* in standard from $$4x^{2}+y^{2}-8x-20y+40 = 0 $$

**Answer**

$4x^{2}+y^{2}-8x-20y+40 = 0 $

$4x^{2}-8x+y^{2}-20y=-40$

$4(x^{2}-2x)+(y^{2}-20y)=-40$

$4(x^{2}-2x+1)+(y^{2}-20y+100)=-40+4+100$

$4(x-1)^2+(y-10)^2 = 64$

$\frac{1}{16}(x-1)^2+\frac{1}{64}(y-10)^2 = 1$

$\frac{(x-1)^2}{{4}^2}+\frac{(y-10)^2}{{8}^2} = 1$