What is x^2-4y^2+2x-16y-19=0 ?

The solution to x^2-4y^2+2x-16y-19=0 is Hyperbola with (h,k)=(-1,-2),a=2,b=1

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x^2-4y^2+2x-16y-19=0

x^{2} - 4 y^{2} + 2 x - 16 y - 19 = 0

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

Solution steps

x^{2} - 4 y^{2} + 2 x - 16 y - 19 = 0

Rewrite

x^{2} - 4 y^{2} + 2 x - 16 y - 19 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

(x^{2} - 4 x) - (y^{2} + 4 y) = 1

6 x^{2} - 3 y^{2} + 36 x + 30 y = 39

y^{2} - 4 = 9 x^{2}

(4 - 4 x)^{2} - 4 (2 k (x) + 2) (k (x) - 2) = 0

4 x^{2} - y^{2} - 32 x - 2 y = - 59

What is x^2-4y^2+2x-16y-19=0 ?
The solution to x^2-4y^2+2x-16y-19=0 is Hyperbola with (h,k)=(-1,-2),a=2,b=1