A horizontal hyperbola has eccentricity √10/2 and contains (2√2,3). Find its equation.

01 / Standard#Your turn

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

Official paper · jm01-2024 · II.5(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

Relate the two squared parameters.
$\frac{b^2}{a^2}=\frac52-1=\frac32$
Solve using the point condition.
$\frac8{a^2}-\frac9{(3/2)a^2}=1\implies a^2=2,\ b^2=3$

x²/2−y²/3=1.

Checks and common pitfalls: For a hyperbola, c²=a²+b².

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Relate the two squared parameters.
$\frac{b^2}{a^2}=\frac52-1=\frac32$
Solve using the point condition.
$\frac8{a^2}-\frac9{(3/2)a^2}=1\implies a^2=2,\ b^2=3$

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

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