What is x^2-2x+4y^2-24y+33=0 ?

The solution to x^2-2x+4y^2-24y+33=0 is Ellipse with (h,k)=(1,3),a=2,b=1

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x^2-2x+4y^2-24y+33=0

x^{2} - 2 x + 4 y^{2} - 24 y + 33 = 0

(h, k) = (1, 3), a = 2, b = 1

Solution steps

x^{2} - 2 x + 4 y^{2} - 24 y + 33 = 0

Rewrite

x^{2} - 2 x + 4 y^{2} - 24 y + 33 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, 3), a = 2, b = 1

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, 3), a = 2, b = 1

\frac{x ^{2}}{1} + \frac{y ^{2}}{5} = 1

4 x^{2} + y^{2} + 56 = 4 y - 56 x

\frac{( x - 3 ) ^{2}}{49} + \frac{( y + 6 ) ^{2}}{100} = 1

\frac{( x - ( - 2 ) ) ^{2}}{9} + \frac{( y - 3 ) ^{2}}{25} = 1

(\frac{x ^{2}}{15}) + (\frac{( y - 8 ) ^{2}}{49}) = 1

What is x^2-2x+4y^2-24y+33=0 ?
The solution to x^2-2x+4y^2-24y+33=0 is Ellipse with (h,k)=(1,3),a=2,b=1