For m>0, find the non-origin intersection P of y=mx and y²=4x.

01 / Standard#Your turn

Official paper · jm02-2022 · 3(c)(i) · PDF 5

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Substitute y=mx.

Hint 2

Remove the x=0 root already identified.

Worked solution

P=(4/m²,4/m).

Checks and common pitfalls: m>0 ensures the expressions are defined and P is not the origin.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Factor the intersection equation.
$m^2x^2=4x\iff x(m^2x-4)=0$
Use the nonzero root and recover y.
$P=(4/m^2,4/m)$

Think first. Reveal a hint when the class is ready.

2022 JM02