What is 4x^2-y^2+8x+6y-6=0 ?

The solution to 4x^2-y^2+8x+6y-6=0 is Hyperbola with (h,k)=(-1,3),a= 1/2 ,b=1

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4x^2-y^2+8x+6y-6=0

4 x^{2} - y^{2} + 8 x + 6 y - 6 = 0

(h, k) = (- 1, 3), a = \frac{1}{2}, b = 1

Solution steps

4 x^{2} - y^{2} + 8 x + 6 y - 6 = 0

Rewrite

4 x^{2} - y^{2} + 8 x + 6 y - 6 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 1, 3), a = \frac{1}{2}, b = 1

8 x^{2} - 4 y^{2} - 16 x - 24 = 0

\frac{( y - 1 ) ^{2}}{4} - \frac{( x + 8 ) ^{2}}{25} = 1

3 x^{2} - 4 y^{2} + 3 x + 16 y - 18 = 0

\frac{( x - 5 ) ^{2}}{8 ^{2}} - \frac{( y - 2 ) ^{2}}{6 ^{2}} = 1

4 y^{2} - x^{2} = 900

What is 4x^2-y^2+8x+6y-6=0 ?
The solution to 4x^2-y^2+8x+6y-6=0 is Hyperbola with (h,k)=(-1,3),a= 1/2 ,b=1