The horizontal ellipse has right focus F₁ on y=x−1. Find both foci.

01 / Standard#Your turn

\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,\quad a>b>0

Official paper · jm02-2025 · 3(b) · PDF 5

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Both foci lie on the x-axis.

Hint 2

The other focus is its reflection about the origin.

Worked solution

F₁=(1,0), F₂=(−1,0).

Checks and common pitfalls: a>b establishes a horizontal major axis.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Set y=0 in the line.
$0=x-1\implies F_1=(1,0)$
Use the central symmetry of the ellipse.
$F_2=(-1,0)$

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

2025 JM02