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}

(x^{2} + y^{2} - 16 x + 8 y + 80) = 4 x^{2} + 4 y^{2} - 16 x - 32 y + 80

4 y^{(2)} + 16 x^{(2)} - 36 x - 20 y + 18 = 0

1 - x^{2} - \frac{y ^{2}}{4} \geq 0

x, (x - k (x)^{2}) = k (x)^{2} + 2 x + x^{2}

7 x + 14 y - 8 x^{2} - 8 y^{2} = 15

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)