What is 2x^2+y^2=2y+1 ?

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

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2x^2+y^2=2y+1

2 x^{2} + y^{2} = 2 y + 1

(h, k) = (0, 1), a = 1, b = 2

Solution steps

2 x^{2} + y^{2} = 2 y + 1

Rewrite

2 x^{2} + y^{2} = 2 y + 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 1), a = 1, b = 2

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 1), b = 2, a = 1

\frac{( x + 2 ) ^{2}}{4} + \frac{( y - 4 ) ^{2}}{16} = 1

\frac{x ^{2}}{25} + \frac{y ^{2}}{49} = 1

\frac{x ^{2}}{15} + \frac{y ^{2}}{17} = 1

4 x^{2} + y^{2} + 40 x + 6 y + 95 = 0

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

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