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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

\frac{x ^{2}}{\frac{25}{4}} + \frac{( y + \frac{5}{2} ) ^{2}}{\frac{9}{4}} = 1

\frac{x ^{2}}{9} + \frac{y ^{2}}{4} = y + 6

2 (x^{2} + 3 x) + y (3 y - 1) = - 4

4 x^{2} - 2 x + 9 y^{2} + 6 y = 41

25 \cdot x^{2} + 9 \cdot y^{2} = 225

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