What is x^{(2)}-y^{(2)}=25 ?

The solution to x^{(2)}-y^{(2)}=25 is Hyperbola with (h,k)=(0,0),a=5,b=5

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x^{(2)}-y^{(2)}=25

x^{(2)} - y^{(2)} = 25

(h, k) = (0, 0), a = 5, b = 5

Solution steps

x^{2} - y^{2} = 25

Rewrite

x^{2} - y^{2} = 25

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = 5, b = 5

x^{(2)} - y^{(2)} = 20

x^{2} - 16 y^{2} = 144

\frac{( x + 4 ) ^{2}}{4} - \frac{( y - 8 ) ^{2}}{16} = 1

25 x^{2} - 16 y^{2} - 400 = 0

x^{2} - \frac{y ^{2}}{10} = 5

What is x^{(2)}-y^{(2)}=25 ?
The solution to x^{(2)}-y^{(2)}=25 is Hyperbola with (h,k)=(0,0),a=5,b=5