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

The solution to x^2-6y+y^2=0 is Ellipse with (h,k)=(0,3),a=3,b=3

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

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

(h, k) = (0, 3), a = 3, b = 3

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{3 ^{2}} + \frac{( y - 3 ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 3), a = 3, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 3), b = 3, a = 3

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

\frac{( ( x + 5 ) ^{2} )}{10} + \frac{( ( y + 4 ) ^{2} )}{8} = 1

3 x^{2} + y^{2} = 25

2 x^{2} + 9 y^{2} - 12 x - 18 y + 9 = 0

\frac{x ^{2}}{100} + \frac{y ^{2}}{144} = 1

What is x^2-6y+y^2=0 ?
The solution to x^2-6y+y^2=0 is Ellipse with (h,k)=(0,3),a=3,b=3