What is x^2-y^2=2^{100} ?

The solution to x^2-y^2=2^{100} is Hyperbola with (h,k)=(0,0),a=2^{50},b=2^{50}

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x^2-y^2=2^{100}

x^{2} - y^{2} = 2^{100}

(h, k) = (0, 0), a = 2^{50}, b = 2^{50}

Solution steps

x^{2} - y^{2} = 2^{100}

Rewrite

x^{2} - y^{2} = 2^{100}

in the form of a standard hyperbola equation

\frac{( x - 0 ) ^{2}}{( 2 ^{50} ) ^{2}} - \frac{( y - 0 ) ^{2}}{( 2 ^{50} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = 2^{50}, b = 2^{50}

x^{2} - y^{2} + x - y - 44 = 0

4 x^{2} - 25 y^{2} + 24 x + 100 y + 36 = 0

16 x^{2} - 4 y^{2} = 49

16 x^{2} - 9 y^{2} - 36 y = 108

x^{2} + y^{2} - 8 x^{2} + 7 = 0

What is x^2-y^2=2^{100} ?
The solution to x^2-y^2=2^{100} is Hyperbola with (h,k)=(0,0),a=2^{50},b=2^{50}