Answer
$\dfrac{(x+1)^2}{4}-\dfrac{(y+2)^2}{9}=1$
Work Step by Step
Center: $(-1,-2) \implies h=-1,k=-2$ and Vertices: $(-3,-2), (1,-2)$
This yields: $ h-a=-3 \implies a=2$ and $ b=2$
Standard Equation for a hyperbola when the hyperbola opens to the left is: $\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1$
We have $ a^2=4; b^2 =4$
So, the equation for the hyperbola is:
$\dfrac{(x+1)^2}{4}-\dfrac{(y+2)^2}{9}=1$
