What is a^2+b^2i^2=9 ?

The solution to a^2+b^2i^2=9 is Hyperbola with (h,k)=(0,0),a=3,b=3

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a^2+b^2i^2=9

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

(h, k) = (0, 0), a = 3, b = 3

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( a - 0 ) ^{2}}{3 ^{2}} - \frac{( b - 0 ) ^{2}}{3 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = 3, b = 3

8 x^{2} - 2 y^{2} - 16 x - 16 y - 32 = 0

9 x^{2} - 25 y^{2} - 90 x + 50 y - 25 = 0

\frac{( y + 5 ) ^{2}}{81} - \frac{( x + 8 ) ^{2}}{9} = 1

x^{2} - y^{2} - 1 = 3 x - 3 y

3 x^{2} - 3 y^{2} + 2 x + 14 y + 24 = 0

What is a^2+b^2i^2=9 ?
The solution to a^2+b^2i^2=9 is Hyperbola with (h,k)=(0,0),a=3,b=3