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

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

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

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

(h, k) = (\frac{1}{2}, 0), a = \frac{1}{2}, b = \frac{1}{2}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (\frac{1}{2}, 0), a = \frac{1}{2}, b = \frac{1}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (\frac{1}{2}, 0), b = \frac{1}{2}, a = \frac{1}{2}

\frac{( x + 7 ) ^{2}}{6} + \frac{( y + 7 ) ^{2}}{5} = 1

4 x^{2} - 16 + y^{2} + 2 y = - 1

9 x^{2} + 49 y^{2} = 1

8 x^{2} + 18 y^{2} + 32 x - 36 y - 22 = 0

4 x^{2} + 2 y^{2} = 19

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