-y=x^2-y^2

Solution

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

\frac{x ^{2}}{4} - \frac{y ^{2}}{12} = 1

x^{2} + 2 x - y^{2} + 1 - 4 = 0

8 x^{2} - 4 y^{2} + 10 x - 6 y - 8 = 0

\frac{x ^{2}}{4} - \frac{y ^{2}}{5} = 1

\frac{( x - 5 ) ^{2}}{16} - \frac{( y + 7 ) ^{2}}{9} = - 1

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