Consider the curve with equation f(x)=3x2. The point P(a,3a2) lies on the curve.
a. Find the gradient to the curve at x=a.
b. Show that the equation of the tangent line to the curve at point P(a,3a2) has equation y=6ax−3a2.
c. Given that the tangent line passes through the point A(0,−3) find the possible values of a.
d. Hence, find the equations of the tangent lines passing through A(0,−3).