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

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

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

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

(h, k) = (2, 1), a = 23, b = 3

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (2, 1), a = 23, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (2, 1), a = 23, b = 3

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

(x - 0.017)^{2} + (\frac{y ^{2}}{( 0.999 ) ^{2}}) = 1

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

(4 x^{2} - 8 x) + (9 y^{2} - 36 y) = - 4

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

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