What is 9(X^2+6X)-4Y^2=-45 ?

The solution to 9(X^2+6X)-4Y^2=-45 is Hyperbola with (h,k)=(-3,0),a=2,b=3

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9(X^2+6X)-4Y^2=-45

9 (X^{2} + 6 X) - 4 Y^{2} = - 45

(h, k) = (- 3, 0), a = 2, b = 3

Solution steps

9 (X^{2} + 6 X) - 4 Y^{2} = - 45

Rewrite

9 (X^{2} + 6 X) - 4 Y^{2} = - 45

in the form of a standard hyperbola equation

\frac{( X - ( - 3 ) ) ^{2}}{2 ^{2}} - \frac{( Y - 0 ) ^{2}}{3 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 3, 0), a = 2, b = 3

4 y^{2} - x^{2} + 2 x + 16 y + 7 = 0

(x - 3) (x + 1) = yy

x^{2} - 25 y^{2} = 25

x^{2} + 6 x - 4 y^{2} - 8 y + 9 = 0

y^{2} = 3 6^{2} + x^{2}

What is 9(X^2+6X)-4Y^2=-45 ?
The solution to 9(X^2+6X)-4Y^2=-45 is Hyperbola with (h,k)=(-3,0),a=2,b=3