What is x^2+y^2+(x-1)^2=1 ?

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

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x^2+y^2+(x-1)^2=1

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

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

Solution steps

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

Rewrite

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

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 ^{2}}{8 ^{2}} + \frac{y ^{2}}{7 ^{2}} = 1

\frac{x ^{2}}{25} + \frac{y ^{2}}{6 ^{2}} = 1

\frac{( X + 3 ) ^{2}}{49} + \frac{( Y + 2 ) ^{2}}{36} = 1

16 x^{2} + 25 y^{2} + 224 + 250 y - 191 = 0

\frac{( x + 3 ) ^{2}}{16} + \frac{( y + 2 ) ^{2}}{9} = 1

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