What is x^2+4y^2+4x+8y-8=0 ?

The solution to x^2+4y^2+4x+8y-8=0 is Ellipse with (h,k)=(-2,-1),a=4,b=2

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x^2+4y^2+4x+8y-8=0

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

(h, k) = (- 2, - 1), a = 4, b = 2

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 2, - 1), a = 4, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 2, - 1), a = 4, b = 2

x^{2} + 6 y^{2} = 15

x^{2} = - y^{2} - 8 y

(2 x + 4 y)^{2} = 16 x y + 16

\frac{( x + 2 ) ^{2}}{4} + \frac{( y - 1 ) ^{2}}{25} = 1

\frac{x ^{2}}{9} + \frac{y ^{2}}{4} = 2

What is x^2+4y^2+4x+8y-8=0 ?
The solution to x^2+4y^2+4x+8y-8=0 is Ellipse with (h,k)=(-2,-1),a=4,b=2