Practice variation 1 of 3
Polynomial roots — Hyperbola $y=2/x$
Your question
Consider the hyperbola and the circle , where is a positive constant.
(i) Show that the -coordinates of any points of intersection are zeros of .
(ii) Hence, by solving , find the exact value of such that the hyperbola and circle intersect at only one point.
This practice question was inspired by Question 14(b) 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.
Before you check
- Have you stated every choice or assumption?
- Can another student follow each line?
- Did you verify the final result independently?