What is x^{(2)}-y^{(2)}=10(x-y)+1 ?

The solution to x^{(2)}-y^{(2)}=10(x-y)+1 is Hyperbola with (h,k)=(5,5),a=1,b=1

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x^{(2)}-y^{(2)}=10(x-y)+1

x^{(2)} - y^{(2)} = 10 (x - y) + 1

(h, k) = (5, 5), a = 1, b = 1

Solution steps

x^{2} - y^{2} = 10 (x - y) + 1

Rewrite

x^{2} - y^{2} - 10 (x - y) - 1 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (5, 5), a = 1, b = 1

\frac{x ^{2}}{2 0 ^{2}} - \frac{y ^{2}}{1 5 ^{2}} = 1

7 y^{2} - 14 x^{2} = 98

(\frac{x ^{2}}{36}) - \frac{y ^{2}}{25} = 1

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

- 4 x^{2} + 5 y^{2} + 8 x - 30 y + 21 = 0

What is x^{(2)}-y^{(2)}=10(x-y)+1 ?
The solution to x^{(2)}-y^{(2)}=10(x-y)+1 is Hyperbola with (h,k)=(5,5),a=1,b=1