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

\frac{x ^{2} - 8 x + 16}{16} - \frac{y ^{2} + 4 y - 4}{9} = 0

50 x^{2} - 25 y^{2} + 144 x - 68 y - 75 = 0

4 x^{2} - y^{2} - 20 x - 10 y + 25 = 0

\frac{x ^{2}}{0.0008} - \frac{y ^{2}}{0.999} = 1

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

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