What is 3y^2-4x^2-6y-24x-105=0 ?

The solution to 3y^2-4x^2-6y-24x-105=0 is Hyperbola with (h,k)=(-3,1),a=2sqrt(6),b=3sqrt(2)

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3y^2-4x^2-6y-24x-105=0

3 y^{2} - 4 x^{2} - 6 y - 24 x - 105 = 0

(h, k) = (- 3, 1), a = 26, b = 32

Solution steps

3 y^{2} - 4 x^{2} - 6 y - 24 x - 105 = 0

Rewrite

3 y^{2} - 4 x^{2} - 6 y - 24 x - 105 = 0

in the form of a standard hyperbola equation

\frac{( y - 1 ) ^{2}}{( 2 6 ) ^{2}} - \frac{( x - ( - 3 ) ) ^{2}}{( 3 2 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 3, 1), a = 26, b = 32

\frac{y ^{2}}{36} - \frac{x ^{2}}{13} = 1

x, 4 k (x)^{2} - 4 x (x + 1) = 7

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

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

4 x^{2} - y^{2} = 36

What is 3y^2-4x^2-6y-24x-105=0 ?
The solution to 3y^2-4x^2-6y-24x-105=0 is Hyperbola with (h,k)=(-3,1),a=2sqrt(6),b=3sqrt(2)