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

The solution to 2x^2-9y^2+4x-36y-16=0 is Hyperbola with (h,k)=(-1,-2),a=sqrt(2),b=3

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

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

(x + 5)^{2} - (y - 3)^{2} = 16

25 x^{2} - 49 y^{2} - 100 x + 294 y + 884 = 0

x^{2} - 2 x - y^{2} - 6 y + 9 = 0

\frac{y ^{2}}{36} - \frac{x ^{2}}{64} = 1

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

What is 2x^2-9y^2+4x-36y-16=0 ?
The solution to 2x^2-9y^2+4x-36y-16=0 is Hyperbola with (h,k)=(-1,-2),a=sqrt(2),b=3