What is x^2-6x+8y-y^2=0 ?

The solution to x^2-6x+8y-y^2=0 is Hyperbola with (h,k)=(3,4),a=sqrt(7),b=sqrt(7)

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x^2-6x+8y-y^2=0

x^{2} - 6 x + 8 y - y^{2} = 0

(h, k) = (3, 4), a = 7, b = 7

Solution steps

x^{2} - 6 x + 8 y - y^{2} = 0

Rewrite

x^{2} - 6 x + 8 y - y^{2} = 0

in the form of a standard hyperbola equation

\frac{( y - 4 ) ^{2}}{( 7 ) ^{2}} - \frac{( x - 3 ) ^{2}}{( 7 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (3, 4), a = 7, b = 7

c^{2} = 5^{2} + a^{2}

9 x^{2} - 18 x - 4 y^{2} - 16 y = 43

\frac{y ^{2}}{25} - \frac{x ^{2}}{49} = 1

3 x^{2} - 2 y^{2} + 3 x - 4 y - 12 = 0

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

What is x^2-6x+8y-y^2=0 ?
The solution to x^2-6x+8y-y^2=0 is Hyperbola with (h,k)=(3,4),a=sqrt(7),b=sqrt(7)