What is 3x^2-y^2-24x-8y+61=0 ?

The solution to 3x^2-y^2-24x-8y+61=0 is Hyperbola with (h,k)=(4,-4),a=sqrt(29),b=sqrt(29/3)

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3x^2-y^2-24x-8y+61=0

3 x^{2} - y^{2} - 24 x - 8 y + 61 = 0

(h, k) = (4, - 4), a = 29, b = \frac{29}{3}

Solution steps

3 x^{2} - y^{2} - 24 x - 8 y + 61 = 0

Rewrite

3 x^{2} - y^{2} - 24 x - 8 y + 61 = 0

in the form of a standard hyperbola equation

\frac{( y - ( - 4 ) ) ^{2}}{( 29 ) ^{2}} - \frac{( x - 4 ) ^{2}}{( \frac{29}{3} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (4, - 4), a = 29, b = \frac{29}{3}

(y + 2)^{2} = 2 x^{2} + 8

\frac{( y - 8 ) ^{2}}{25} - \frac{( x - 12 ) ^{2}}{16} = 1

(a - b) (a + b) = 3000

y^{2} = x^{2} + 576

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

What is 3x^2-y^2-24x-8y+61=0 ?
The solution to 3x^2-y^2-24x-8y+61=0 is Hyperbola with (h,k)=(4,-4),a=sqrt(29),b=sqrt(29/3)