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

The solution to ((x^2-y^2-1))/2 =x^2+y^2-1 is Ellipse with (h,k)=(0,0),a=1,b=sqrt(1/3)

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

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

(h, k) = (0, 0), a = 1, b = \frac{1}{3}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 1, b = \frac{1}{3}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 1, b = \frac{1}{3}

What is ((x^2-y^2-1))/2 =x^2+y^2-1 ?
The solution to ((x^2-y^2-1))/2 =x^2+y^2-1 is Ellipse with (h,k)=(0,0),a=1,b=sqrt(1/3)