All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

(i)

(ii)

At P,

Equation of tangent:

At D,

Therefore, .

Midpoint of

As varies,

We have that

Then,

Thus,

Personal Comments:

This questions test students on their understanding of parametric equations and finding gradient. Find the cartesian equation can be slightly tricky if a student hasn’t been exposed to such questions before.