What is 4x^2+8x-4y^2+12y-3=0 ?

The solution to 4x^2+8x-4y^2+12y-3=0 is Hyperbola with (h,k)=(-1, 3/2),a=sqrt(1/2),b=sqrt(1/2)

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4x^2+8x-4y^2+12y-3=0

4 x^{2} + 8 x - 4 y^{2} + 12 y - 3 = 0

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

Solution steps

4 x^{2} + 8 x - 4 y^{2} + 12 y - 3 = 0

Rewrite

4 x^{2} + 8 x - 4 y^{2} + 12 y - 3 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

\frac{( x + 4 ) ^{2}}{16} - \frac{( y - 2 ) ^{2}}{36} = 1

12 y^{2} + 72 y - 4 x^{2} + 16 x + 44 = 0

(x - 1)^{2} - (y - 4)^{2} = 16

y^{2} = x^{2} + 289

- 3 y^{2} + 18 x^{2} = - y - 2

What is 4x^2+8x-4y^2+12y-3=0 ?
The solution to 4x^2+8x-4y^2+12y-3=0 is Hyperbola with (h,k)=(-1, 3/2),a=sqrt(1/2),b=sqrt(1/2)