What is x^2-4y^2+2x-16y+13=0 ?

The solution to x^2-4y^2+2x-16y+13=0 is Hyperbola with (h,k)=(-1,-2),a=sqrt(7),b=2sqrt(7)

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x^2-4y^2+2x-16y+13=0

x^{2} - 4 y^{2} + 2 x - 16 y + 13 = 0

(h, k) = (- 1, - 2), a = 7, b = 27

Solution steps

x^{2} - 4 y^{2} + 2 x - 16 y + 13 = 0

Rewrite

x^{2} - 4 y^{2} + 2 x - 16 y + 13 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 1, - 2), a = 7, b = 27

(x - 1)^{2} - (y - 10)^{2} = - 40

\frac{( y + 9 ) ^{2}}{49} - \frac{( x - 1 ) ^{2}}{9} = 1

y^{2} + 7 = x^{2} - 8

\frac{( a ^{2} + b ^{2} )}{2} - 2 (a^{2} - b^{2}) = - 15

4 x^{2} + 8 x - y^{2} + 2 y = - 5

What is x^2-4y^2+2x-16y+13=0 ?
The solution to x^2-4y^2+2x-16y+13=0 is Hyperbola with (h,k)=(-1,-2),a=sqrt(7),b=2sqrt(7)