What is y^2-x^2+5x-4y+3=0 ?

The solution to y^2-x^2+5x-4y+3=0 is Hyperbola with (h,k)=(5/2 ,2),a=(sqrt(21))/2 ,b=(sqrt(21))/2

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y^2-x^2+5x-4y+3=0

y^{2} - x^{2} + 5 x - 4 y + 3 = 0

(h, k) = (\frac{5}{2}, 2), a = \frac{21}{2}, b = \frac{21}{2}

Solution steps

y^{2} - x^{2} + 5 x - 4 y + 3 = 0

Rewrite

y^{2} - x^{2} + 5 x - 4 y + 3 = 0

in the form of a standard hyperbola equation

\frac{( x - \frac{5}{2} ) ^{2}}{( \frac{21}{2} ) ^{2}} - \frac{( y - 2 ) ^{2}}{( \frac{21}{2} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (\frac{5}{2}, 2), a = \frac{21}{2}, b = \frac{21}{2}

\frac{( x + 2 ) ^{2}}{4} - \frac{( y - 2 ) ^{2}}{25} = 1

2 x^{2} - 3 y^{2} - 12 x - 24 y + 60 = 0

9 x^{2} - 16 y^{2} - 36 = 0

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

\frac{y ^{2}}{25} - \frac{x ^{2}}{25} = 1

What is y^2-x^2+5x-4y+3=0 ?
The solution to y^2-x^2+5x-4y+3=0 is Hyperbola with (h,k)=(5/2 ,2),a=(sqrt(21))/2 ,b=(sqrt(21))/2