What is x^2-2x-4y^2-40y=103 ?

The solution to x^2-2x-4y^2-40y=103 is Hyperbola with (h,k)=(1,-5),a=2,b=1

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x^2-2x-4y^2-40y=103

x^{2} - 2 x - 4 y^{2} - 40 y = 103

(h, k) = (1, - 5), a = 2, b = 1

Solution steps

x^{2} - 2 x - 4 y^{2} - 40 y = 103

Rewrite

x^{2} - 2 x - 4 y^{2} - 40 y = 103

in the form of a standard hyperbola equation

\frac{( x - 1 ) ^{2}}{2 ^{2}} - \frac{( y - ( - 5 ) ) ^{2}}{1 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (1, - 5), a = 2, b = 1

16 X^{2} - 25 Y^{2} + 96 X + 544 = 0

7 x^{2} - 12 y^{2} - 14 x + 24 y - 28 = 0

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

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

2 x^{2} - y^{2} + 12 x + 8 y + 6 = 0

What is x^2-2x-4y^2-40y=103 ?
The solution to x^2-2x-4y^2-40y=103 is Hyperbola with (h,k)=(1,-5),a=2,b=1