What is 2(x^2-10x)-9(y^2-8y)=-16 ?

The solution to 2(x^2-10x)-9(y^2-8y)=-16 is Hyperbola with (h,k)=(5,4),a=(sqrt(110))/3 ,b=sqrt(55)

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2(x^2-10x)-9(y^2-8y)=-16

2 (x^{2} - 10 x) - 9 (y^{2} - 8 y) = - 16

(h, k) = (5, 4), a = \frac{110}{3}, b = 55

Solution steps

2 (x^{2} - 10 x) - 9 (y^{2} - 8 y) = - 16

Rewrite

2 (x^{2} - 10 x) - 9 (y^{2} - 8 y) = - 16

in the form of a standard hyperbola equation

\frac{( y - 4 ) ^{2}}{( \frac{110}{3} ) ^{2}} - \frac{( x - 5 ) ^{2}}{( 55 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (5, 4), a = \frac{110}{3}, b = 55

\frac{x ^{2}}{36} - \frac{y ^{2}}{100} = 1

\frac{( x - 5 ) ^{2}}{4} - \frac{( y - 3 ) ^{2}}{4} = 1

x^{2} - 4 y^{2} + 2 x - 16 y + 13 = 0

(x - 1)^{2} - (y - 10)^{2} = - 40

\frac{( y + 9 ) ^{2}}{49} - \frac{( x - 1 ) ^{2}}{9} = 1

What is 2(x^2-10x)-9(y^2-8y)=-16 ?
The solution to 2(x^2-10x)-9(y^2-8y)=-16 is Hyperbola with (h,k)=(5,4),a=(sqrt(110))/3 ,b=sqrt(55)