What is x^2-4x+4+y^2=(x^2)/4-(16x)/4+64/4 ?

The solution to x^2-4x+4+y^2=(x^2)/4-(16x)/4+64/4 is Ellipse with (h,k)=(0,0),a=4,b=2sqrt(3)

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x^2-4x+4+y^2=(x^2)/4-(16x)/4+64/4

x^{2} - 4 x + 4 + y^{2} = \frac{x ^{2}}{4} - \frac{16 x}{4} + \frac{64}{4}

(h, k) = (0, 0), a = 4, b = 23

Solution steps

x^{2} - 4 x + 4 + y^{2} = \frac{x ^{2}}{4} - \frac{16 x}{4} + \frac{64}{4}

Rewrite

x^{2} - 4 x + 4 + y^{2} - \frac{x ^{2}}{4} + \frac{16 x}{4} - \frac{64}{4} = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{4 ^{2}} + \frac{( y - 0 ) ^{2}}{( 2 3 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 4, b = 23

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 4, b = 23

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

x^{2} + 12 y^{2} - 12 x - 48 y + 72 = 0

220 x^{2} + 256 y^{2} - 660 x - 3025 = 0

x^{2} + y^{2} + 12 y^{2} - 108 = 0

4 x^{2} + 8 y^{2} = 16

What is x^2-4x+4+y^2=(x^2)/4-(16x)/4+64/4 ?
The solution to x^2-4x+4+y^2=(x^2)/4-(16x)/4+64/4 is Ellipse with (h,k)=(0,0),a=4,b=2sqrt(3)