What is x^2+y^2= 1/2 (y+1)^2 ?

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

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x^2+y^2= 1/2 (y+1)^2

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

(h, k) = (0, 1), a = 1, b = 2

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 1), a = 1, b = 2

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 1), b = 2, a = 1

\frac{( x - 3 ) ^{2}}{225} + \frac{( y + 9 ) ^{2}}{121} = 1

\frac{x ^{2}}{15} + \frac{y ^{2}}{45} = 1

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

\frac{( x + 11 ) ^{2}}{100} + \frac{( y - 4 ) ^{2}}{1 9 ^{2}} = 1

4 x^{2} + 3 y^{2} + 4 x = 1

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