If $k$ be the length of the latus rectum of the hyperbola $16x^2 - 9y^2 + 32x + 36y - 164 = 0$, then find $3k/8$.
Step-by-Step Solution
Key Concept: For a standard hyperbola, identify the center and parameters to compute derived quantities.
The hyperbola $\frac{(x+1)^2}{9} - \frac{(y-2)^2}{16} = 1$ has center at $(-1, 2)$. The parameter $k$ is found from the geometric properties of the hyperbola, yielding $k = \frac{2 \times 16}{3} = \frac{32}{3}$.
Correct Answer: 4