2023 HSC Mathematics Extension 1
Question 11(a):
Coordinate geometry
The parametric equations of a line are given below.
Find the Cartesian equation of this line in the form .
How to recognise this question
Question type: coordinate geometry
- The command and notation point to coordinate geometry.
- The requested response is a worked solution.
How to handle it: convert between parametric and Cartesian forms carefully, noting the direction of the parameter.
Watch out: Do not select a formula until its domain, interval, sign and units match the question.
Step-by-step answer
- From , solve for the parameter: .
- Substitute into : .
- So and .
- NESA: 2 marks for correct solution; 1 mark for obtaining in terms of , or equivalent merit.
Common mistake: choosing a familiar formula before checking that its conditions, signs, interval and units match this question.
The paper records 2 total marks for this group. Where the official marking guide provides useful partial-credit criteria, those criteria are stated in the steps above.
Try your hand at it again by answering these questions
Question 1
Eliminate from , and write .
Question 2
Find the Cartesian form of , .
Question 3
Eliminate from , .