What is 9x^2-16y^2+36x+96y-252=0 ?

The solution to 9x^2-16y^2+36x+96y-252=0 is Hyperbola with (h,k)=(-2,3),a=4,b=3

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9x^2-16y^2+36x+96y-252=0

9 x^{2} - 16 y^{2} + 36 x + 96 y - 252 = 0

(h, k) = (- 2, 3), a = 4, b = 3

Solution steps

9 x^{2} - 16 y^{2} + 36 x + 96 y - 252 = 0

Rewrite

9 x^{2} - 16 y^{2} + 36 x + 96 y - 252 = 0

in the form of a standard hyperbola equation

\frac{( x - ( - 2 ) ) ^{2}}{4 ^{2}} - \frac{( y - 3 ) ^{2}}{3 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 2, 3), a = 4, b = 3

x^{2} - 6 x - 2 y^{2} + 7 = 0

\frac{( x - 3 ) ^{2}}{16} - \frac{( y + 1 ) ^{2}}{9} = 1

(\frac{y}{100})^{2} - \frac{x ^{2}}{49} = 1

(x + y) (x - y) = 60.49

9 x^{2} - 4 y^{2} = 144

What is 9x^2-16y^2+36x+96y-252=0 ?
The solution to 9x^2-16y^2+36x+96y-252=0 is Hyperbola with (h,k)=(-2,3),a=4,b=3