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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

7 p - p^{2} = 9 p + q^{2} - 16 - 5 q^{2} + 6

x^{2} - y^{2} < 8

9 y^{2} - 16 x^{2} = 1

4 x^{2} - 16 y^{2} - 10 x + 21 y - 27 = 0

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

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