What is y^2-4x^2-2y+24x=51 ?

The solution to y^2-4x^2-2y+24x=51 is Hyperbola with (h,k)=(3,1),a=4,b=2

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y^2-4x^2-2y+24x=51

y^{2} - 4 x^{2} - 2 y + 24 x = 51

(h, k) = (3, 1), a = 4, b = 2

Solution steps

y^{2} - 4 x^{2} - 2 y + 24 x = 51

Rewrite

y^{2} - 4 x^{2} - 2 y + 24 x = 51

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (3, 1), a = 4, b = 2

\frac{( x - 1 ) ^{2}}{36} - \frac{( y + 2 ) ^{2}}{25} = 1

\frac{x ^{2}}{3 0 ^{2}} - \frac{y ^{2}}{4 4 ^{2}} = 1

y^{2} - x^{2} = 8

y^{2} - x^{2} = 5

\frac{x ^{2}}{6} - \frac{y ^{2}}{9} = 1

What is y^2-4x^2-2y+24x=51 ?
The solution to y^2-4x^2-2y+24x=51 is Hyperbola with (h,k)=(3,1),a=4,b=2