Use A=(0,−1) and the foci to determine the positive semiaxes a,b.

01 / Standard#Your turn

\frac{x^2}{a^2}+\frac{y^2}{b^2}=1

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

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Substitute the point on the y-axis.

Hint 2

Use a²=b²+c² with focal distance c=1.

Worked solution

a=√2, b=1; ellipse x²/2+y²=1.

Checks and common pitfalls: Choose positive semiaxes as stipulated.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
A lies on the ellipse, giving b²=1.
$\frac1{b^2}=1,\quad b>0\implies b=1$
Recover a from the focal relation.
$a^2=b^2+c^2=2\implies a=\sqrt2$

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

2025 JM02