The vertical ellipse has eccentricity √2/2 and contains (2√2,4). Find its equation.

01 / Standard#Your turn

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

Official paper · jm01-2022 · II.3(a) · PDF 4

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Use e²=1−b²/a².

Hint 2

Substitute the given point.

Worked solution

The squared semiaxes satisfy b²=a²/2.
$1-\frac{b^2}{a^2}=1/2$
Use the point condition to find both.
$\frac8{a^2/2}+\frac{16}{a^2}=1\implies a^2=32,\quad b^2=16$

x²/16+y²/32=1.

Checks and common pitfalls: The larger denominator lies under y² for a vertical major axis.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
The squared semiaxes satisfy b²=a²/2.
$1-\frac{b^2}{a^2}=1/2$
Use the point condition to find both.
$\frac8{a^2/2}+\frac{16}{a^2}=1\implies a^2=32,\quad b^2=16$

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

2022 JM01