What is x^2+4y^2-2x+4y+1=0 ?

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

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x^2+4y^2-2x+4y+1=0

x^{2} + 4 y^{2} - 2 x + 4 y + 1 = 0

(h, k) = (1, - \frac{1}{2}), a = 1, b = \frac{1}{2}

Solution steps

x^{2} + 4 y^{2} - 2 x + 4 y + 1 = 0

Rewrite

x^{2} + 4 y^{2} - 2 x + 4 y + 1 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, - \frac{1}{2}), a = 1, b = \frac{1}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, - \frac{1}{2}), a = 1, b = \frac{1}{2}

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