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← 2023 HSC Extension 1 paper Question 11(a)

Variation 3 · answer guide

Coordinate geometry — Through origin style

Question

Eliminate from , .

This practice question was inspired by Question 11(a) in the 2023 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.

Step by step

  1. Set up the solution: convert between parametric and Cartesian forms carefully, noting the direction of the parameter..
  2. Finish the calculation, then check that the result meets the question’s conditions..
  3. State the final answer clearly in the form the question requested.So .

Common mistake: changing so many features that the new example no longer tests the same mathematical idea.

Verification: At , is the -intercept.

Any mark labels are a TestMum study aid, not an official NESA marking allocation.

← Back to 2023 HSC Extension 1 paper Question 11(a)