What is 4x^2-y^2+8x+4y=15 ?

The solution to 4x^2-y^2+8x+4y=15 is Hyperbola with (h,k)=(-1,2),a=(sqrt(15))/2 ,b=sqrt(15)

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4x^2-y^2+8x+4y=15

4 x^{2} - y^{2} + 8 x + 4 y = 15

(h, k) = (- 1, 2), a = \frac{15}{2}, b = 15

Solution steps

4 x^{2} - y^{2} + 8 x + 4 y = 15

Rewrite

4 x^{2} - y^{2} + 8 x + 4 y = 15

in the form of a standard hyperbola equation

\frac{( x - ( - 1 ) ) ^{2}}{( \frac{15}{2} ) ^{2}} - \frac{( y - 2 ) ^{2}}{( 15 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 1, 2), a = \frac{15}{2}, b = 15

y^{2} - 2 y = x^{2} - x - 1

\frac{( x - 5 ) ^{2}}{25} - \frac{( y + 2 ) ^{2}}{16} = 1

2 x^{2} - 2 y^{2} = 12

\frac{x ^{2}}{9} - \frac{y ^{2}}{14} = 1

\frac{( y + 7 ) ^{2}}{9} - \frac{( x - 5 ) ^{2}}{16} = 1

What is 4x^2-y^2+8x+4y=15 ?
The solution to 4x^2-y^2+8x+4y=15 is Hyperbola with (h,k)=(-1,2),a=(sqrt(15))/2 ,b=sqrt(15)