What is z^2+10^2=2+q^2+(96^2)/2 ?

The solution to z^2+10^2=2+q^2+(96^2)/2 is Hyperbola with (h,k)=(0,0),a=sqrt(4510),b=sqrt(4510)

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z^2+10^2=2+q^2+(96^2)/2

z^{2} + 1 0^{2} = 2 + q^{2} + \frac{9 6 ^{2}}{2}

(h, k) = (0, 0), a = 4510, b = 4510

Solution steps

z^{2} + 1 0^{2} = 2 + q^{2} + \frac{9 6 ^{2}}{2}

Rewrite

z^{2} + 1 0^{2} - 2 - q^{2} - \frac{9 6 ^{2}}{2} = 0

in the form of a standard hyperbola equation

\frac{( z - 0 ) ^{2}}{( 4510 ) ^{2}} - \frac{( q - 0 ) ^{2}}{( 4510 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = 4510, b = 4510

(x^{2} + 2 x - 2 y^{2}) = 0

\frac{( x - 4 ) ^{2}}{25} - \frac{( y + 8 ) ^{2}}{49} = 1

\frac{( x - 4 ) ^{2}}{9} - \frac{( y + 5 ) ^{2}}{16} = 1

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

144 y^{2} - 25 x^{2} = 3600

What is z^2+10^2=2+q^2+(96^2)/2 ?
The solution to z^2+10^2=2+q^2+(96^2)/2 is Hyperbola with (h,k)=(0,0),a=sqrt(4510),b=sqrt(4510)