What is x^{(2)}-y^{(2)}=20 ?

The solution to x^{(2)}-y^{(2)}=20 is Hyperbola with (h,k)=(0,0),a=2sqrt(5),b=2sqrt(5)

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

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

(h, k) = (0, 0), a = 25, b = 25

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = 25, b = 25

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

5 x^{2} - 3 y^{2} - 20 x - 18 y - 22 = 0

What is x^{(2)}-y^{(2)}=20 ?
The solution to x^{(2)}-y^{(2)}=20 is Hyperbola with (h,k)=(0,0),a=2sqrt(5),b=2sqrt(5)