What is 9x^2-4y^2+54x+16y+29=0 ?

The solution to 9x^2-4y^2+54x+16y+29=0 is Hyperbola with (h,k)=(-3,2),a=2,b=3

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9x^2-4y^2+54x+16y+29=0

9 x^{2} - 4 y^{2} + 54 x + 16 y + 29 = 0

(h, k) = (- 3, 2), a = 2, b = 3

Solution steps

9 x^{2} - 4 y^{2} + 54 x + 16 y + 29 = 0

Rewrite

9 x^{2} - 4 y^{2} + 54 x + 16 y + 29 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 3, 2), a = 2, b = 3

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

\frac{( y - 0 ) ^{2}}{3 ^{2}} - \frac{( x - 2 ) ^{2}}{4 ^{2}} = 1

\frac{( y + 3 ) ^{2}}{9} - \frac{( x - 2 ) ^{2}}{16} = 1

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

2 x^{2} - 5 y^{2} = 52

What is 9x^2-4y^2+54x+16y+29=0 ?
The solution to 9x^2-4y^2+54x+16y+29=0 is Hyperbola with (h,k)=(-3,2),a=2,b=3