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

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

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

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

(h, k) = (0, \frac{1}{2}), a = \frac{1}{2}, b = \frac{1}{2}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, \frac{1}{2}), a = \frac{1}{2}, b = \frac{1}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, \frac{1}{2}), b = \frac{1}{2}, a = \frac{1}{2}

64 y^{2} + 300 x + 100 x^{2} = - 81 + 256 y

x^{2} + y^{2} - 9 - 4 x^{2} - 9 y^{2} - 36 = 0

- 16 x^{2} - 9 y^{2} = 144

7 x^{2} + 3 y^{2} = 55

\frac{( x - 2 ) ^{2}}{6} + \frac{( y - 6 2 ) ^{2}}{8} = 1

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