What is 4x^2-32x-y^2-4y+24=0 ?

The solution to 4x^2-32x-y^2-4y+24=0 is Hyperbola with (h,k)=(4,-2),a=3,b=6

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4x^2-32x-y^2-4y+24=0

4 x^{2} - 32 x - y^{2} - 4 y + 24 = 0

(h, k) = (4, - 2), a = 3, b = 6

Solution steps

4 x^{2} - 32 x - y^{2} - 4 y + 24 = 0

Rewrite

4 x^{2} - 32 x - y^{2} - 4 y + 24 = 0

in the form of a standard hyperbola equation

\frac{( x - 4 ) ^{2}}{3 ^{2}} - \frac{( y - ( - 2 ) ) ^{2}}{6 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (4, - 2), a = 3, b = 6

(x - 2)^{2} - (y - 4)^{2} = 81

x^{2} - 9 y^{2} - 2 x + 54 y - 116 = 0

9 x^{2} - 4 y^{2} - 18 x + 24 y + 45 = 0

\frac{y ^{2}}{25} - \frac{( x - 4 ) ^{2}}{16} = 1

x^{2} - 2 y^{2} + 6 x + 4 y + 5 = 0

What is 4x^2-32x-y^2-4y+24=0 ?
The solution to 4x^2-32x-y^2-4y+24=0 is Hyperbola with (h,k)=(4,-2),a=3,b=6