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

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

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

\frac{2 x - x ^{2} - y ^{2}}{x ^{2} + y ^{2} - x} \leq 0

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

Solution steps

\frac{2 x - x ^{2} - y ^{2}}{x ^{2} + y ^{2} - x} \leq 0

Rewrite

\frac{2 x - x ^{2} - y ^{2}}{x ^{2} + y ^{2} - x} \leq 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

x^{2} + 2 - 6 x = - 5 z^{2} + 2

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

x, x^{2} + 5 Y (x)^{2} + 2 x - 30 Y + 36 = 0

\frac{( x - 2 ) ^{2}}{9} + \frac{( y - 3 ) ^{2}}{49} = 1

\frac{( x - 1 ) ^{2}}{8} + \frac{( y + \frac{3}{2} ) ^{2}}{4} = 1

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