What is 25x^2-9y^2-54y=306 ?

The solution to 25x^2-9y^2-54y=306 is Hyperbola with (h,k)=(0,-3),a=3,b=5

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25x^2-9y^2-54y=306

25 x^{2} - 9 y^{2} - 54 y = 306

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

Solution steps

25 x^{2} - 9 y^{2} - 54 y = 306

Rewrite

25 x^{2} - 9 y^{2} - 54 y = 306

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

16 x^{2} - 9 y^{2} - 96 x + 9 y - 36 = 0

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

x^{2} - 8 y^{2} - 6 x - 22 y + 4 = 0

\frac{( y - 11 ) ^{2}}{16} - \frac{( x + 5 ) ^{2}}{36} = 1

- 25 x^{2} + y^{2} = 25

What is 25x^2-9y^2-54y=306 ?
The solution to 25x^2-9y^2-54y=306 is Hyperbola with (h,k)=(0,-3),a=3,b=5