What is x^2-3y^2-8x-18y=14 ?

The solution to x^2-3y^2-8x-18y=14 is Hyperbola with (h,k)=(4,-3),a=sqrt(3),b=1

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x^2-3y^2-8x-18y=14

x^{2} - 3 y^{2} - 8 x - 18 y = 14

(h, k) = (4, - 3), a = 3, b = 1

Solution steps

x^{2} - 3 y^{2} - 8 x - 18 y = 14

Rewrite

x^{2} - 3 y^{2} - 8 x - 18 y = 14

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (4, - 3), a = 3, b = 1

[f (x)]^{2} = 4 x^{2} - x + 3

2 x^{2} - 3 y^{2} - 6 = 0

\frac{( x - 6 ) ^{2}}{48} - (y - 2)^{2} = 1

1680 = \frac{a}{b} a - b

a^{2} + 9 = c^{2}

What is x^2-3y^2-8x-18y=14 ?
The solution to x^2-3y^2-8x-18y=14 is Hyperbola with (h,k)=(4,-3),a=sqrt(3),b=1