What is x^2+y^2-6+2y+6=0 ?

The solution to x^2+y^2-6+2y+6=0 is Ellipse with (h,k)=(0,-1),a=1,b=1

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x^2+y^2-6+2y+6=0

x^{2} + y^{2} - 6 + 2 y + 6 = 0

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

Solution steps

x^{2} + y^{2} - 6 + 2 y + 6 = 0

Rewrite

x^{2} + y^{2} - 6 + 2 y + 6 = 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

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

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

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

5 x^{2} + 9 y^{2} - 30 x = 0

\frac{( x + 5 ) ^{2}}{97} + \frac{( y + 2 ) ^{2}}{36} = 1

What is x^2+y^2-6+2y+6=0 ?
The solution to x^2+y^2-6+2y+6=0 is Ellipse with (h,k)=(0,-1),a=1,b=1