You are given the parametric equations $x=10-t^2,\;\;y=t^3-12t.$

(a) List all of the points $(x, y)$ where the tangent line is horizontal. In entering your answer, list the points starting with the smallest value of $x$. If two or more points share the same value of $x$, list those points starting with the smallest value of $y$. If any blanks are unused, type an upper-case "N" in them.

Point 1: $(x, y) =$ ( , )

Point 2: $(x, y) =$ ( , )

Point 3: $(x, y) =$ ( , )

(b) List all of the points $(x, y)$ where the tangent line is vertical. In entering your answer, list the points starting with the smallest value of $x$. If two or more points share the same value of $x$, list those points starting with the smallest value of $y$. If any blanks are unused, type an upper-case "N" in them.

Point 1: $(x, y) =$ ( , )

Point 2: $(x, y) =$ ( , )

Point 3: $(x, y) =$ ( , )