What is 9x^2-4y^2-72x+8y+176=0 ?

The solution to 9x^2-4y^2-72x+8y+176=0 is Hyperbola with (h,k)=(4,1),a=3,b=2

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9x^2-4y^2-72x+8y+176=0

9 x^{2} - 4 y^{2} - 72 x + 8 y + 176 = 0

(h, k) = (4, 1), a = 3, b = 2

Solution steps

9 x^{2} - 4 y^{2} - 72 x + 8 y + 176 = 0

Rewrite

9 x^{2} - 4 y^{2} - 72 x + 8 y + 176 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (4, 1), a = 3, b = 2

\frac{( y - k ) ^{2}}{a ^{2}} - \frac{( x - h ) ^{2}}{b ^{2}} = 1

x, (x - 2)^{2} + (x - 3)^{2} = r (x)^{2}

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

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

\frac{y ^{2}}{36} - \frac{x ^{2}}{16} = 1

What is 9x^2-4y^2-72x+8y+176=0 ?
The solution to 9x^2-4y^2-72x+8y+176=0 is Hyperbola with (h,k)=(4,1),a=3,b=2