What is 6x^{(2)}-5y^{(2)}+24x+20y-56=0 ?

The solution to 6x^{(2)}-5y^{(2)}+24x+20y-56=0 is Hyperbola with (h,k)=(-2,2),a=sqrt(10),b=2sqrt(3)

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6x^{(2)}-5y^{(2)}+24x+20y-56=0

6 x^{(2)} - 5 y^{(2)} + 24 x + 20 y - 56 = 0

(h, k) = (- 2, 2), a = 10, b = 23

Solution steps

6 x^{2} - 5 y^{2} + 24 x + 20 y - 56 = 0

Rewrite

6 x^{2} - 5 y^{2} + 24 x + 20 y - 56 = 0

in the form of a standard hyperbola equation

\frac{( x - ( - 2 ) ) ^{2}}{( 10 ) ^{2}} - \frac{( y - 2 ) ^{2}}{( 2 3 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 2, 2), a = 10, b = 23

\frac{x ^{2}}{49} - \frac{( y + 2 ) ^{2}}{79} = 1

- \frac{x ^{2}}{144} + \frac{y ^{2}}{25} = 1

\frac{( x - 4 ) ^{2}}{16} - \frac{( y + 2 ) ^{2}}{25} = 1

y^{2} = \frac{4 x ^{2}}{9} - 9

\frac{( y - 3 ) ^{2}}{49} - \frac{( x + 1 ) ^{2}}{16} = 1

What is 6x^{(2)}-5y^{(2)}+24x+20y-56=0 ?
The solution to 6x^{(2)}-5y^{(2)}+24x+20y-56=0 is Hyperbola with (h,k)=(-2,2),a=sqrt(10),b=2sqrt(3)