What is 3a^2-20b^2-100=0 ?

The solution to 3a^2-20b^2-100=0 is Hyperbola with (h,k)=(0,0),a=(10)/(sqrt(3)),b=sqrt(5)

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3a^2-20b^2-100=0

3 a^{2} - 20 b^{2} - 100 = 0

(h, k) = (0, 0), a = \frac{10}{3}, b = 5

Solution steps

3 a^{2} - 20 b^{2} - 100 = 0

Rewrite

3 a^{2} - 20 b^{2} - 100 = 0

in the form of a standard hyperbola equation

\frac{( a - 0 ) ^{2}}{( \frac{10}{3} ) ^{2}} - \frac{( b - 0 ) ^{2}}{( 5 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = \frac{10}{3}, b = 5

x^{2} - 6 x + 8 y - y^{2} = 0

c^{2} = 5^{2} + a^{2}

9 x^{2} - 18 x - 4 y^{2} - 16 y = 43

\frac{y ^{2}}{25} - \frac{x ^{2}}{49} = 1

3 x^{2} - 2 y^{2} + 3 x - 4 y - 12 = 0

What is 3a^2-20b^2-100=0 ?
The solution to 3a^2-20b^2-100=0 is Hyperbola with (h,k)=(0,0),a=(10)/(sqrt(3)),b=sqrt(5)