What is a^2-4b^2=15 ?

The solution to a^2-4b^2=15 is Hyperbola with (h,k)=(0,0),a=sqrt(15),b=(sqrt(15))/2

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a^2-4b^2=15

a^{2} - 4 b^{2} = 15

(h, k) = (0, 0), a = 15, b = \frac{15}{2}

Solution steps

a^{2} - 4 b^{2} = 15

Rewrite

a^{2} - 4 b^{2} = 15

in the form of a standard hyperbola equation

\frac{( a - 0 ) ^{2}}{( 15 ) ^{2}} - \frac{( b - 0 ) ^{2}}{( \frac{15}{2} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = 15, b = \frac{15}{2}

9 x^{2} - 4 y^{2} - 18 x + 8 y + 10 = 0

x^{2} - y^{2} - 4 x + 3 = 0

1 + y^{2} = x^{2} (\frac{10}{4})

(\frac{x ^{2}}{16}) - (\frac{( y + 4 ) ^{2}}{81}) = 1

16 x^{2} + 96 x - 9 y^{2} + 54 y + 207 = 0

What is a^2-4b^2=15 ?
The solution to a^2-4b^2=15 is Hyperbola with (h,k)=(0,0),a=sqrt(15),b=(sqrt(15))/2