What is 9x^2+36x-4y^2-16y-16=0 ?

The solution to 9x^2+36x-4y^2-16y-16=0 is Hyperbola with (h,k)=(-2,-2),a=2,b=3

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9x^2+36x-4y^2-16y-16=0

9 x^{2} + 36 x - 4 y^{2} - 16 y - 16 = 0

(h, k) = (- 2, - 2), a = 2, b = 3

Solution steps

9 x^{2} + 36 x - 4 y^{2} - 16 y - 16 = 0

Rewrite

9 x^{2} + 36 x - 4 y^{2} - 16 y - 16 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 2, - 2), a = 2, b = 3

x^{(2)} - y^{(2)} = 10 (x - y) + 1

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

7 y^{2} - 14 x^{2} = 98

(\frac{x ^{2}}{36}) - \frac{y ^{2}}{25} = 1

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

What is 9x^2+36x-4y^2-16y-16=0 ?
The solution to 9x^2+36x-4y^2-16y-16=0 is Hyperbola with (h,k)=(-2,-2),a=2,b=3