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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

\frac{x ^{2} + y ^{2}}{x ^{2} + ( y + 1 ) ^{2}} = 16

200 = \frac{1000}{1 + x ^{2} + y ^{2}}

\frac{( x - 8 ) ^{2}}{42} + \frac{( y + 7 ) ^{2}}{16} = 1

2 x^{2} + 2 y^{2} - 8 y = 0

6 x^{2} + 9 y^{2} + 54 y = 60 x - 87

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