we need to find the tangents to the curve passing through .
(1)Let the tangent pass through the point such that lies on , then the slope of the tangent is (using (i)). Since lies on the tangent, the equation of the tangent is or .
(2)Also note that slope, . We also know that (we found it in point 1 using differentiation).
Relating these two:
Solving this with quadratic formula : . Since there are two values of , there must be two equations.
(3)Put the values of a in any of the two equations (in point 1) and you will get: and .