What is 4x^2-y^2-24x-4y+28=0 ?

The solution to 4x^2-y^2-24x-4y+28=0 is Hyperbola with (h,k)=(3,-2),a=1,b=2

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4x^2-y^2-24x-4y+28=0

4 x^{2} - y^{2} - 24 x - 4 y + 28 = 0

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

Solution steps

4 x^{2} - y^{2} - 24 x - 4 y + 28 = 0

Rewrite

4 x^{2} - y^{2} - 24 x - 4 y + 28 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

y, x^{2} = y^{2}

x^{2} + y^{2} + 10 x - 4 y - 7 = 0

y^{2} = - 10 x

x^{2} = 8 y

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

What is 4x^2-y^2-24x-4y+28=0 ?
The solution to 4x^2-y^2-24x-4y+28=0 is Hyperbola with (h,k)=(3,-2),a=1,b=2