What is y^2-4y+x^2=0 ?

The solution to y^2-4y+x^2=0 is Ellipse with (h,k)=(0,2),a=2,b=2

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y^2-4y+x^2=0

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

(h, k) = (0, 2), a = 2, b = 2

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 2), a = 2, b = 2

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 2), b = 2, a = 2

9 x^{2} - 72 x + y^{2} + 10 y + 160 = 0

\frac{x ^{2}}{3} + \frac{y ^{2}}{6} = 1

(x - 5)^{2} + \frac{y ^{2}}{25} = 1

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

\frac{( x ^{2} )}{9} + \frac{( y ^{2} )}{16} = 1

What is y^2-4y+x^2=0 ?
The solution to y^2-4y+x^2=0 is Ellipse with (h,k)=(0,2),a=2,b=2