What is x^2-y^2-3x+4y=0 ?

The solution to x^2-y^2-3x+4y=0 is Hyperbola with (h,k)=(3/2 ,2),a=(sqrt(7))/2 ,b=(sqrt(7))/2

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

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

(h, k) = (\frac{3}{2}, 2), a = \frac{7}{2}, b = \frac{7}{2}

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( y - 2 ) ^{2}}{( \frac{7}{2} ) ^{2}} - \frac{( x - \frac{3}{2} ) ^{2}}{( \frac{7}{2} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (\frac{3}{2}, 2), a = \frac{7}{2}, b = \frac{7}{2}

(x - y) (x + y + 6) = - 9

\frac{( x - 1 ) ^{2}}{4} - \frac{( y - 2 ) ^{2}}{16} = 1

x^{2} - y^{2} - 2 x - 6 y - 12 = 0

16 x^{2} - 9 y^{2} + 96 = 0

\frac{( x - 3 ) ^{2}}{9} - \frac{( y + 2 ) ^{2}}{4} = 1

What is x^2-y^2-3x+4y=0 ?
The solution to x^2-y^2-3x+4y=0 is Hyperbola with (h,k)=(3/2 ,2),a=(sqrt(7))/2 ,b=(sqrt(7))/2