What is 9x^2-4y^2-36x+16y=0 ?

The solution to 9x^2-4y^2-36x+16y=0 is Hyperbola with (h,k)=(2,2),a=(2sqrt(5))/3 ,b=sqrt(5)

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9x^2-4y^2-36x+16y=0

9 x^{2} - 4 y^{2} - 36 x + 16 y = 0

(h, k) = (2, 2), a = \frac{2 5}{3}, b = 5

Solution steps

9 x^{2} - 4 y^{2} - 36 x + 16 y = 0

Rewrite

9 x^{2} - 4 y^{2} - 36 x + 16 y = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (2, 2), a = \frac{2 5}{3}, b = 5

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

12 x^{2} + 6 y^{2} + 3 = 10 x^{2} + 10 y^{2} + 4

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

4 x^{2} - 12 y^{2} + 8 x + 2 y = 2

- 25 x^{2} + 4 y^{2} - 100 = 0

What is 9x^2-4y^2-36x+16y=0 ?
The solution to 9x^2-4y^2-36x+16y=0 is Hyperbola with (h,k)=(2,2),a=(2sqrt(5))/3 ,b=sqrt(5)