What is 9x^2-4y^2+54x+16y+66=0 ?

The solution to 9x^2-4y^2+54x+16y+66=0 is Hyperbola with (h,k)=(-3,2),a= 1/2 ,b= 1/3

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9x^2-4y^2+54x+16y+66=0

9 x^{2} - 4 y^{2} + 54 x + 16 y + 66 = 0

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

Solution steps

9 x^{2} - 4 y^{2} + 54 x + 16 y + 66 = 0

Rewrite

9 x^{2} - 4 y^{2} + 54 x + 16 y + 66 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

x^{2} = (13 y^{2} + 1)

a^{2} - b^{2} = 424

a^{2} - b^{2} = 415

4 y^{2} - 24 y - 2 x^{2} + 20 = 2

9 (x^{2} - 2 x) - 4 (y^{2} + 4 y) = - 29

What is 9x^2-4y^2+54x+16y+66=0 ?
The solution to 9x^2-4y^2+54x+16y+66=0 is Hyperbola with (h,k)=(-3,2),a= 1/2 ,b= 1/3