What is 4x^2-y^2+16x+16y-9=0 ?

The solution to 4x^2-y^2+16x+16y-9=0 is Hyperbola with (h,k)=(-2,8),a=sqrt(39),b=(sqrt(39))/2

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4x^2-y^2+16x+16y-9=0

4 x^{2} - y^{2} + 16 x + 16 y - 9 = 0

(h, k) = (- 2, 8), a = 39, b = \frac{39}{2}

Solution steps

4 x^{2} - y^{2} + 16 x + 16 y - 9 = 0

Rewrite

4 x^{2} - y^{2} + 16 x + 16 y - 9 = 0

in the form of a standard hyperbola equation

\frac{( y - 8 ) ^{2}}{( 39 ) ^{2}} - \frac{( x - ( - 2 ) ) ^{2}}{( \frac{39}{2} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 2, 8), a = 39, b = \frac{39}{2}

36 x^{2} - y^{2} - 24 x + 6 y - 41 = 0

\frac{x ^{2}}{4} + \frac{x}{2} - \frac{y ^{2}}{9} - \frac{2 y}{9} + \frac{1}{6} = 0

9 x^{2} - 9 y^{2} - 6 x + 24 y = 19

\frac{y ^{2}}{56} - \frac{x ^{2}}{56} = 1

\frac{( y - 1 ) ^{2}}{9} - \frac{( x - 3 ) ^{2}}{4} = 1

What is 4x^2-y^2+16x+16y-9=0 ?
The solution to 4x^2-y^2+16x+16y-9=0 is Hyperbola with (h,k)=(-2,8),a=sqrt(39),b=(sqrt(39))/2