What is 9x^2-16y^2-108x+128y+212=0 ?

The solution to 9x^2-16y^2-108x+128y+212=0 is Hyperbola with (h,k)=(6,4),a=3,b=4

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9x^2-16y^2-108x+128y+212=0

9 x^{2} - 16 y^{2} - 108 x + 128 y + 212 = 0

(h, k) = (6, 4), a = 3, b = 4

Solution steps

9 x^{2} - 16 y^{2} - 108 x + 128 y + 212 = 0

Rewrite

9 x^{2} - 16 y^{2} - 108 x + 128 y + 212 = 0

in the form of a standard hyperbola equation

\frac{( y - 4 ) ^{2}}{3 ^{2}} - \frac{( x - 6 ) ^{2}}{4 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (6, 4), a = 3, b = 4

x^{2} - 4 y^{2} = 36

- 25 x^{2} + 9 y^{2} = 225

9 y^{2} - 25 x^{2} = 225

\frac{( x - 5 ) ^{2}}{4} - \frac{( y + 1 ) ^{2}}{49} = 1

4 (y - 3)^{2} - 9 (x - 2)^{2} = 36

What is 9x^2-16y^2-108x+128y+212=0 ?
The solution to 9x^2-16y^2-108x+128y+212=0 is Hyperbola with (h,k)=(6,4),a=3,b=4