What is x^2-y^2+3x-4y=6 ?

The solution to x^2-y^2+3x-4y=6 is Hyperbola with (h,k)=(-3/2 ,-2),a=(sqrt(17))/2 ,b=(sqrt(17))/2

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x^2-y^2+3x-4y=6

x^{2} - y^{2} + 3 x - 4 y = 6

(h, k) = (- \frac{3}{2}, - 2), a = \frac{17}{2}, b = \frac{17}{2}

Solution steps

x^{2} - y^{2} + 3 x - 4 y = 6

Rewrite

x^{2} - y^{2} + 3 x - 4 y = 6

in the form of a standard hyperbola equation

\frac{( x - ( - \frac{3}{2} ) ) ^{2}}{( \frac{17}{2} ) ^{2}} - \frac{( y - ( - 2 ) ) ^{2}}{( \frac{17}{2} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- \frac{3}{2}, - 2), a = \frac{17}{2}, b = \frac{17}{2}

4 x^{2} - 34 y - 5 y^{2} + 36 = 0

9 x^{2} - 4 y^{2} + 24 \leq 0

x^{2} - 16 y^{2} = 64

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

4 x^{2} - 625 \cdot y^{2} + 2 \cdot y - 1 = 0

What is x^2-y^2+3x-4y=6 ?
The solution to x^2-y^2+3x-4y=6 is Hyperbola with (h,k)=(-3/2 ,-2),a=(sqrt(17))/2 ,b=(sqrt(17))/2