What is 3y^2-4x^2-8x-24y-40=0 ?

The solution to 3y^2-4x^2-8x-24y-40=0 is Hyperbola with (h,k)=(-1,4),a=2sqrt(7),b=sqrt(21)

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3y^2-4x^2-8x-24y-40=0

3 y^{2} - 4 x^{2} - 8 x - 24 y - 40 = 0

(h, k) = (- 1, 4), a = 27, b = 21

Solution steps

3 y^{2} - 4 x^{2} - 8 x - 24 y - 40 = 0

Rewrite

3 y^{2} - 4 x^{2} - 8 x - 24 y - 40 = 0

in the form of a standard hyperbola equation

\frac{( y - 4 ) ^{2}}{( 2 7 ) ^{2}} - \frac{( x - ( - 1 ) ) ^{2}}{( 21 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 1, 4), a = 27, b = 21

4 x^{2} - 2 y^{2} + 36 y + 24 x = 36

9 x^{2} - 16 y^{2} - 108 x + 128 y = - 212

- x^{2} - 16 x + 4 y^{2} - 12 y + 16 = 0

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

\frac{( x - 3 ) ^{2}}{9} - \frac{( y - 2 ) ^{2}}{16} = 1

What is 3y^2-4x^2-8x-24y-40=0 ?
The solution to 3y^2-4x^2-8x-24y-40=0 is Hyperbola with (h,k)=(-1,4),a=2sqrt(7),b=sqrt(21)