In the analytic plane
$$x y ^ { 2 } - x ^ { 3 } y - 6 = 0$$
Given that the tangent line passing through the point $\mathbf { P } \left( \mathbf { x } _ { 0 } , \mathbf { y } _ { 0 } \right)$ on the curve given by the equation is parallel to the x-axis, what is $\mathrm { x } _ { 0 }$?
A) $- 3$
B) $- 2$
C) $\frac { - 3 } { 2 }$

In the rectangular coordinate plane
$$y ^ { 2 } + \sin \left( x ^ { 2 } - 1 \right) = 4$$
What is the slope of the tangent line to the curve given by this equation at the point $\mathbf { P } ( - \mathbf { 1 } , - \mathbf { 2 } )$?
A) - 1
B) $\frac { 1 } { 2 }$
C) 2
D) $\frac { - 1 } { 2 }$