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

The solution to x^2+4y^2+4y=8 is Ellipse with (h,k)=(0,-1/2),a=3,b= 3/2

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

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

(h, k) = (0, - \frac{1}{2}), a = 3, b = \frac{3}{2}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{3 ^{2}} + \frac{( y - ( - \frac{1}{2} ) ) ^{2}}{( \frac{3}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, - \frac{1}{2}), a = 3, b = \frac{3}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, - \frac{1}{2}), a = 3, b = \frac{3}{2}

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

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

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

7 x^{2} + 16 y^{2} = 7

y^{2} + 4 x^{2} + 24 x - 16 y = - 84

What is x^2+4y^2+4y=8 ?
The solution to x^2+4y^2+4y=8 is Ellipse with (h,k)=(0,-1/2),a=3,b= 3/2