What is (u+v)(u-v)=v ?

The solution to (u+v)(u-v)=v is Hyperbola with (h,k)=(0,-1/2),a= 1/2 ,b= 1/2

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(u+v)(u-v)=v

(u + v) (u - v) = v

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

Solution steps

(u + v) (u - v) = v

Rewrite

(u + v) (u - v) - v = 0

in the form of a standard hyperbola equation

\frac{( v - ( - \frac{1}{2} ) ) ^{2}}{( \frac{1}{2} ) ^{2}} - \frac{( u - 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}}{15} - \frac{y ^{2}}{5} = 1

10 x^{2} - 7 y^{2} - 30 x + 14 y - 5 = 0

x^{2} - y^{2} + 6 x + 10 y = 2

\frac{( y + 3 ) ^{2}}{16} - \frac{( x + 1 ) ^{2}}{4} = 1

4 y^{2} - 2 x^{2} - 4 y - 15 = 0

What is (u+v)(u-v)=v ?
The solution to (u+v)(u-v)=v is Hyperbola with (h,k)=(0,-1/2),a= 1/2 ,b= 1/2