What is y^2-4x^2-4y+24x=48 ?

The solution to y^2-4x^2-4y+24x=48 is Hyperbola with (h,k)=(3,2),a=4,b=2

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y^2-4x^2-4y+24x=48

y^{2} - 4 x^{2} - 4 y + 24 x = 48

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

Solution steps

y^{2} - 4 x^{2} - 4 y + 24 x = 48

Rewrite

y^{2} - 4 x^{2} - 4 y + 24 x = 48

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

x^{2} - 4 y^{2} + 2 x - 16 y - 19 = 0

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

6 x^{2} - 3 y^{2} + 36 x + 30 y = 39

y^{2} - 4 = 9 x^{2}

(4 - 4 x)^{2} - 4 (2 k (x) + 2) (k (x) - 2) = 0

What is y^2-4x^2-4y+24x=48 ?
The solution to y^2-4x^2-4y+24x=48 is Hyperbola with (h,k)=(3,2),a=4,b=2