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

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

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

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

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

Solution steps

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

Rewrite

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

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

4 x^{2} + 18 y^{2} = 72

(y - 6)^{2} + 8 (x)^{2} = 64

\frac{( x + 1 ) ^{2}}{25} + \frac{( y + 2 ) ^{2}}{49} = 1

9 x^{2} + 4 y^{2} + 18 x - 8 y - 23 = 0

3 x^{2} + 4 y^{2} = 48

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