A slope-3/4 line through the focus meets x²=4y at A,B. Find AB.

01 / Standard#Your turn

Official paper · jm01-2023 · II.2(b) · PDF 4

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

The line equation is y=3x/4+1.

Hint 2

Solve the intersection quadratic.

Worked solution

AB=25/4.

Checks and common pitfalls: The horizontal difference alone is not the chord length.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Find the two points.
$x^2=3x+4\implies x=-1,4;\quad A=(-1,1/4),\ B=(4,4)$
Use the distance formula.
$AB=\sqrt{5^2+(15/4)^2}=25/4$

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

2023 JM01