What is x^2-4y^2-4x+24y+37=0 ?

The solution to x^2-4y^2-4x+24y+37=0 is Hyperbola with (h,k)=(2,3),a=(sqrt(69))/2 ,b=sqrt(69)

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x^2-4y^2-4x+24y+37=0

x^{2} - 4 y^{2} - 4 x + 24 y + 37 = 0

(h, k) = (2, 3), a = \frac{69}{2}, b = 69

Solution steps

x^{2} - 4 y^{2} - 4 x + 24 y + 37 = 0

Rewrite

x^{2} - 4 y^{2} - 4 x + 24 y + 37 = 0

in the form of a standard hyperbola equation

\frac{( y - 3 ) ^{2}}{( \frac{69}{2} ) ^{2}} - \frac{( x - 2 ) ^{2}}{( 69 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (2, 3), a = \frac{69}{2}, b = 69

6 x^{2} - y^{2} - 12 x - 6 y + 5 = 0

4 a 2 - 9 b 2 = (2 a 2 + 3 b 2) (2 a 2 - 3 b 2)

25 x^{2} - 9 y^{2} + 50 x - 36 y - 236 = 0

\frac{( x + 1 ) ^{2}}{16} - \frac{( y - 2 ) ^{2}}{9} = 1

x^{2} - y^{2} - 6 x - 7 = 0

What is x^2-4y^2-4x+24y+37=0 ?
The solution to x^2-4y^2-4x+24y+37=0 is Hyperbola with (h,k)=(2,3),a=(sqrt(69))/2 ,b=sqrt(69)