What is 9x^2-4y^2-72x+16y+92=0 ?

The solution to 9x^2-4y^2-72x+16y+92=0 is Hyperbola with (h,k)=(4,2),a=2,b=3

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9x^2-4y^2-72x+16y+92=0

9 x^{2} - 4 y^{2} - 72 x + 16 y + 92 = 0

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

Solution steps

9 x^{2} - 4 y^{2} - 72 x + 16 y + 92 = 0

Rewrite

9 x^{2} - 4 y^{2} - 72 x + 16 y + 92 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

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

3 x^{2} - 3 y^{2} - 6 x = 0

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

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

\frac{y ^{2}}{4} - \frac{x ^{2}}{32} = 1

What is 9x^2-4y^2-72x+16y+92=0 ?
The solution to 9x^2-4y^2-72x+16y+92=0 is Hyperbola with (h,k)=(4,2),a=2,b=3