What is 2x^2-3y^2+8x+6y-115=0 ?

The solution to 2x^2-3y^2+8x+6y-115=0 is Hyperbola with (h,k)=(-2,1),a=2sqrt(15),b=2sqrt(10)

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2x^2-3y^2+8x+6y-115=0

2 x^{2} - 3 y^{2} + 8 x + 6 y - 115 = 0

(h, k) = (- 2, 1), a = 215, b = 210

Solution steps

2 x^{2} - 3 y^{2} + 8 x + 6 y - 115 = 0

Rewrite

2 x^{2} - 3 y^{2} + 8 x + 6 y - 115 = 0

in the form of a standard hyperbola equation

\frac{( x - ( - 2 ) ) ^{2}}{( 2 15 ) ^{2}} - \frac{( y - 1 ) ^{2}}{( 2 10 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 2, 1), a = 215, b = 210

x^{2} - 4 y^{2} = 5

a^{2} - 4 b^{2} = 15

9 x^{2} - 4 y^{2} - 18 x + 8 y + 10 = 0

x^{2} - y^{2} - 4 x + 3 = 0

1 + y^{2} = x^{2} (\frac{10}{4})

What is 2x^2-3y^2+8x+6y-115=0 ?
The solution to 2x^2-3y^2+8x+6y-115=0 is Hyperbola with (h,k)=(-2,1),a=2sqrt(15),b=2sqrt(10)