What is 9x^2-4y^2+36x+40y-208=0 ?

The solution to 9x^2-4y^2+36x+40y-208=0 is Hyperbola with (h,k)=(-2,5),a=4,b=6

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9x^2-4y^2+36x+40y-208=0

9 x^{2} - 4 y^{2} + 36 x + 40 y - 208 = 0

(h, k) = (- 2, 5), a = 4, b = 6

Solution steps

9 x^{2} - 4 y^{2} + 36 x + 40 y - 208 = 0

Rewrite

9 x^{2} - 4 y^{2} + 36 x + 40 y - 208 = 0

in the form of a standard hyperbola equation

\frac{( x - ( - 2 ) ) ^{2}}{4 ^{2}} - \frac{( y - 5 ) ^{2}}{6 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 2, 5), a = 4, b = 6

x^{2} - 5 y^{2} + 10 y + 4 x - 37 = 0

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

a^{2} - b^{2} = 14

a^{2} - b^{2} = 42

5 y^{2} - 50 y + 44 = 9 x^{2} - 36 x

What is 9x^2-4y^2+36x+40y-208=0 ?
The solution to 9x^2-4y^2+36x+40y-208=0 is Hyperbola with (h,k)=(-2,5),a=4,b=6