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

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

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

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

(h, k) = (0, 2), a = 2, b = 2

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 2), a = 2, b = 2

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 2), b = 2, a = 2

7 x^{2} - 28 x + 4 y^{2} + 8 y = - 4

2 x^{2} + 3 y^{2} - 4 x + 12 y - 20 = 0

\frac{( x - 3 ) ^{2}}{4} + \frac{( y - 3 ) ^{2}}{9} = 1

\frac{x ^{2}}{100} + \frac{y ^{2}}{4} = 1

\frac{( x - 6 ) ^{2}}{100} + \frac{( y + 3 ) ^{2}}{16} = 1

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