What is 5x^2-4y^2+24y-56=0 ?

The solution to 5x^2-4y^2+24y-56=0 is Hyperbola with (h,k)=(0,3),a=2,b=sqrt(5)

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5x^2-4y^2+24y-56=0

5 x^{2} - 4 y^{2} + 24 y - 56 = 0

(h, k) = (0, 3), a = 2, b = 5

Solution steps

5 x^{2} - 4 y^{2} + 24 y - 56 = 0

Rewrite

5 x^{2} - 4 y^{2} + 24 y - 56 = 0

in the form of a standard hyperbola equation

\frac{( x - 0 ) ^{2}}{2 ^{2}} - \frac{( y - 3 ) ^{2}}{( 5 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 3), a = 2, b = 5

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

- 9 x^{2} + y^{2} = 36

4 x^{2} - 16 x - y^{2} - 6 y + 3 = 0

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

\frac{( x - 2 ) ^{2}}{9} - \frac{y ^{2}}{4} = 1

What is 5x^2-4y^2+24y-56=0 ?
The solution to 5x^2-4y^2+24y-56=0 is Hyperbola with (h,k)=(0,3),a=2,b=sqrt(5)