Final Answer:
The equation of the given curve is (y+3)²/1 - (x+5)²/3 = 1.
Step-by-step explanation:
The given equation represents a hyperbola with a horizontal axis. The standard form for such a hyperbola is (y-k)²/a² - (x-h)²/b² = 1, where (h, k) is the center of the hyperbola. Comparing this with the given equation, we can identify that the center of the hyperbola is at (-5, -3).
The denominators 1 and 3 represent the squares of the semi-major and semi-minor axes, respectively. Therefore, the semi-major axis (a) is equal to 1, and the semi-minor axis (b) is equal to √3. The orientation is horizontal since the term involving y comes first.
In conclusion, the equation (y+3)²/1 - (x+5)²/3 = 1 represents a hyperbola centered at (-5, -3) with a semi-major axis of 1 along the y-direction and a semi-minor axis of √3 along the x-direction.