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

Popular >

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}

2 x^{2} + 24 y^{2} + 6 x + 4 y + 1 > 0

16 x^{2} + 4 y^{2} + 96 x - 8 y + 84 = 0

\frac{x ^{2}}{23} + \frac{y ^{2}}{19} = 1

4 x^{2} + 24 x + 36 + 36 y^{2} - 360 y + 756 = 0

\frac{( x - 2 ) ^{2}}{9} + \frac{( y - 3 ) ^{2}}{16} = 1

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