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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

9 x^{(2)} + 16 y^{(2)} - 54 x + 64 y + 1 = 0

\frac{2 y}{1 - x ^{2} - y ^{2}} = 1

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

2 x^{2} + 3 y^{2} + 4 x - 6 y - 1 = 0

y^{2} = 100 - 25 x^{2}

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