What is x^2-y^2-3x+5y-16=0 ?

The solution to x^2-y^2-3x+5y-16=0 is Hyperbola with (h,k)=(3/2 , 5/2),a=2sqrt(3),b=2sqrt(3)

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x^2-y^2-3x+5y-16=0

x^{2} - y^{2} - 3 x + 5 y - 16 = 0

(h, k) = (\frac{3}{2}, \frac{5}{2}), a = 23, b = 23

Solution steps

x^{2} - y^{2} - 3 x + 5 y - 16 = 0

Rewrite

x^{2} - y^{2} - 3 x + 5 y - 16 = 0

in the form of a standard hyperbola equation

\frac{( x - \frac{3}{2} ) ^{2}}{( 2 3 ) ^{2}} - \frac{( y - \frac{5}{2} ) ^{2}}{( 2 3 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (\frac{3}{2}, \frac{5}{2}), a = 23, b = 23

x^{2} - 9 y^{2} - 10 x + 36 y - 2 = 0

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

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

x^{2} + y = x + y^{2} + 2018

\frac{( x - 2 ) ^{2}}{9} - \frac{( y - 1 ) ^{2}}{16} = 1

What is x^2-y^2-3x+5y-16=0 ?
The solution to x^2-y^2-3x+5y-16=0 is Hyperbola with (h,k)=(3/2 , 5/2),a=2sqrt(3),b=2sqrt(3)