What is 2-(2-2x)/(2x-x^2-y^2)=0 ?

The solution to 2-(2-2x)/(2x-x^2-y^2)=0 is Ellipse with (h,k)=(3/2 ,0),a=(sqrt(5))/2 ,b=(sqrt(5))/2

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2-(2-2x)/(2x-x^2-y^2)=0

2 - \frac{2 - 2 x}{2 x - x ^{2} - y ^{2}} = 0

(h, k) = (\frac{3}{2}, 0), a = \frac{5}{2}, b = \frac{5}{2}

Solution steps

2 - \frac{2 - 2 x}{2 x - x ^{2} - y ^{2}} = 0

Rewrite

2 - \frac{2 - 2 x}{2 x - x ^{2} - y ^{2}} = 0

in the form of the standard ellipse equation

\frac{( x - \frac{3}{2} ) ^{2}}{( \frac{5}{2} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{5}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{3}{2}, 0), a = \frac{5}{2}, b = \frac{5}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (\frac{3}{2}, 0), b = \frac{5}{2}, a = \frac{5}{2}

(\frac{x ^{2}}{64}) + (\frac{y ^{2}}{36}) = 1

X^{2} + 2 \cdot Y^{2} - 2 \cdot X - 4 \cdot Y - 8 = 0

\frac{x ^{2}}{21} + \frac{y ^{2}}{25} = 1

4 x^{2} + 16 y^{2} + 16 x + 160 y + 352 = 0

y^{2} = \frac{1 - 4 x ^{2}}{5}

What is 2-(2-2x)/(2x-x^2-y^2)=0 ?
The solution to 2-(2-2x)/(2x-x^2-y^2)=0 is Ellipse with (h,k)=(3/2 ,0),a=(sqrt(5))/2 ,b=(sqrt(5))/2