What is x^2+2x-100y^2-1000y+2401=0 ?

The solution to x^2+2x-100y^2-1000y+2401=0 is Hyperbola with (h,k)=(-1,-5),a=7,b=70

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x^2+2x-100y^2-1000y+2401=0

x^{2} + 2 x - 100 y^{2} - 1000 y + 2401 = 0

(h, k) = (- 1, - 5), a = 7, b = 70

Solution steps

x^{2} + 2 x - 100 y^{2} - 1000 y + 2401 = 0

Rewrite

x^{2} + 2 x - 100 y^{2} - 1000 y + 2401 = 0

in the form of a standard hyperbola equation

\frac{( y - ( - 5 ) ) ^{2}}{7 ^{2}} - \frac{( x - ( - 1 ) ) ^{2}}{7 0 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 1, - 5), a = 7, b = 70

9 x^{2} - 16 y^{2} + 72 x + 96 y + 144 = 0

\frac{y ^{2}}{16} - \frac{x ^{2}}{144} = 1

25 x^{2} - 16 y^{2} + 250 x + 32 y + 109 = 0

16 y^{2} - x^{2} + 2 x + 64 y + 47 = 0

x^{2} + 2 x - y^{2} + 6 y = 15

What is x^2+2x-100y^2-1000y+2401=0 ?
The solution to x^2+2x-100y^2-1000y+2401=0 is Hyperbola with (h,k)=(-1,-5),a=7,b=70