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

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

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

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

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

Solution steps

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

Rewrite

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

\frac{x ^{2}}{36} + \frac{y ^{2}}{20} = 1

\frac{x ^{2}}{4} + \frac{y ^{2}}{7} = 1

16 x^{2} + 9 y^{2} + 160 x - 72 y + 544 = 144

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

7 x^{2} + 18 y^{2} = 63

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