What is 4x^2-9y^2-16x+54y-101=0 ?

The solution to 4x^2-9y^2-16x+54y-101=0 is Hyperbola with (h,k)=(2,3),a=3,b=2

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4x^2-9y^2-16x+54y-101=0

4 x^{2} - 9 y^{2} - 16 x + 54 y - 101 = 0

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

Solution steps

4 x^{2} - 9 y^{2} - 16 x + 54 y - 101 = 0

Rewrite

4 x^{2} - 9 y^{2} - 16 x + 54 y - 101 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

y^{2} - x^{2} = 81

36 + y^{2} = x^{2}

(16) x^{2} - (225) y^{2} + (0) x + (- 2250) y + (2025) = 0

5 x^{2} - 3 y^{2} + 10 x - 12 y = 22

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

What is 4x^2-9y^2-16x+54y-101=0 ?
The solution to 4x^2-9y^2-16x+54y-101=0 is Hyperbola with (h,k)=(2,3),a=3,b=2