What is 9y^2-25x^2+54y+150x=369 ?

The solution to 9y^2-25x^2+54y+150x=369 is Hyperbola with (h,k)=(3,-3),a=5,b=3

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9y^2-25x^2+54y+150x=369

9 y^{2} - 25 x^{2} + 54 y + 150 x = 369

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

Solution steps

9 y^{2} - 25 x^{2} + 54 y + 150 x = 369

Rewrite

9 y^{2} - 25 x^{2} + 54 y + 150 x = 369

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

y^{2} = 8^{2} + x^{2}

a^{2} - b^{2} = - 5

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

- 4 y^{2} + 9 x^{2} - 27 x - 16 y = 24

3 x^{2} - y^{2} - 18 x + 4 y + 20 = 0

What is 9y^2-25x^2+54y+150x=369 ?
The solution to 9y^2-25x^2+54y+150x=369 is Hyperbola with (h,k)=(3,-3),a=5,b=3