\mbox{Question 1C-5:} . . . \mbox{Find all tangent lines through the origin} . . . \mbox{to the graph of }\, y\, =\, 1\, +\, (x\, -\, 1)^2 \mbox{Solution 1C-5:} \mbox{Method 1: }\, y'(x)\, =\, 2(x\, -\, 1),\, \mbox{ so the tangent line through} (a,\, 1\, +\, (a\,...