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

The solution to 2x^2+y^2-2x+4y=2 is Ellipse with (h,k)=(1/2 ,-2),a=(sqrt(13))/2 ,b=sqrt(13/2)

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

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

(h, k) = (\frac{1}{2}, - 2), a = \frac{13}{2}, b = \frac{13}{2}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - \frac{1}{2} ) ^{2}}{( \frac{13}{2} ) ^{2}} + \frac{( y - ( - 2 ) ) ^{2}}{( \frac{13}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{1}{2}, - 2), a = \frac{13}{2}, b = \frac{13}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (\frac{1}{2}, - 2), b = \frac{13}{2}, a = \frac{13}{2}

\frac{( x - 1 ) ^{2}}{4} + \frac{( y - 3 ) ^{2}}{9} = 1

x^{2} + 8 y^{2} = 32

\frac{( x - 1 ) ^{2}}{5 ^{2}} + \frac{( y + 1 ) ^{2}}{3 ^{2}} = 1

\frac{( x - 2 ) ^{2}}{9} + \frac{( y - 3 ) ^{2}}{4} = 1

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

What is 2x^2+y^2-2x+4y=2 ?
The solution to 2x^2+y^2-2x+4y=2 is Ellipse with (h,k)=(1/2 ,-2),a=(sqrt(13))/2 ,b=sqrt(13/2)