What is 500a^2=4368.932+500b^2 ?

The solution to 500a^2=4368.932+500b^2 is Hyperbola with (h,k)=(0,0),a=2.95598…,b=2.95598…

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500a^2=4368.932+500b^2

500 a^{2} = 4368.932 + 500 b^{2}

(h, k) = (0, 0), a = 2.95598 \dots, b = 2.95598 \dots

Solution steps

500 a^{2} = 4368.932 + 500 b^{2}

Rewrite

500 a^{2} = 4368.932 + 500 b^{2}

in the form of a standard hyperbola equation

\frac{( a - 0 ) ^{2}}{2.95598 \dots ^{2}} - \frac{( b - 0 ) ^{2}}{2.95598 \dots ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = 2.95598 \dots, b = 2.95598 \dots

9 a^{2} = 9 b^{2} + 4455

4 x^{2} - y^{2} + 8 y - 32 = 0

4 x^{2} - 4 y^{2} - 32 x + 16 y + 39 = 0

y^{2} - 2 y = x^{2} + 2 x + 1

p^{2} + 2021 = q^{2}

What is 500a^2=4368.932+500b^2 ?
The solution to 500a^2=4368.932+500b^2 is Hyperbola with (h,k)=(0,0),a=2.95598…,b=2.95598…