What is (x+k(x))(x-k(x))=k(x) ?

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

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(x+k(x))(x-k(x))=k(x)

(x + k (x)) (x - k (x)) = k (x)

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

Solution steps

(x + y) (x - y) = y

Rewrite

(x + y) (x - y) - y = 0

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}}{16} - \frac{y ^{2}}{64} = 1

\frac{x ^{2}}{81} - \frac{y ^{2}}{64} = 1

2 y^{2} - 9 x^{2} - 18 x + 20 y + 5 = 0

36 = 9 x^{2} - 4 y^{2}

x^{2} - 4 y^{2} = 3

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