What is y^2-4x^2+4y+24x-41=0 ?

The solution to y^2-4x^2+4y+24x-41=0 is Hyperbola with (h,k)=(3,-2),a=3,b= 3/2

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y^2-4x^2+4y+24x-41=0

y^{2} - 4 x^{2} + 4 y + 24 x - 41 = 0

(h, k) = (3, - 2), a = 3, b = \frac{3}{2}

Solution steps

y^{2} - 4 x^{2} + 4 y + 24 x - 41 = 0

Rewrite

y^{2} - 4 x^{2} + 4 y + 24 x - 41 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (3, - 2), a = 3, b = \frac{3}{2}

x, 3 m (x)^{2} - 2 x^{2} - 1 = 0

5 x^{2} - 4 y^{2} - 80 = 0

y + y^{2} = x^{2} + 4

y + y^{2} = x^{2} + 6

x^{2} - y^{2} = x - y + 2018

What is y^2-4x^2+4y+24x-41=0 ?
The solution to y^2-4x^2+4y+24x-41=0 is Hyperbola with (h,k)=(3,-2),a=3,b= 3/2