What is 2y^2-9x^2-18x+20y+5=0 ?

The solution to 2y^2-9x^2-18x+20y+5=0 is Hyperbola with (h,k)=(-1,-5),a=3sqrt(2),b=2

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2y^2-9x^2-18x+20y+5=0

2 y^{2} - 9 x^{2} - 18 x + 20 y + 5 = 0

(h, k) = (- 1, - 5), a = 32, b = 2

Solution steps

2 y^{2} - 9 x^{2} - 18 x + 20 y + 5 = 0

Rewrite

2 y^{2} - 9 x^{2} - 18 x + 20 y + 5 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 1, - 5), a = 32, b = 2

36 = 9 x^{2} - 4 y^{2}

x^{2} - 4 y^{2} = 3

x^{(2)} + 9 = y^{(2)}

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

a^{2} - b^{2} = 1

What is 2y^2-9x^2-18x+20y+5=0 ?
The solution to 2y^2-9x^2-18x+20y+5=0 is Hyperbola with (h,k)=(-1,-5),a=3sqrt(2),b=2