Standard equation of Ellipse

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Write the equation of the *ellipse* in standard from $$4x^{2}+y^{2}+24x+8y+48 = 0 $$

**Answer**

$4x^{2}+y^{2}+24x+8y+48 = 0 $

$4x^{2}+24x+y^{2}+8y=-48$

$4(x^{2}+6x)+(y^{2}+8y)=-48$

$4(x^{2}+6x+9)+(y^{2}+8y+16)=-48+36+16$

$4(x+3)^2+(y+4)^2 = 4$

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

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