Find the horizontal hyperbola through (2√3,2) with eccentricity √6/2.

01 / Standard#Your turn

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

Official paper · jm01-2026 · II.4(a) · PDF 4

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Relate eccentricity to a and b.

Hint 2

For a hyperbola, c²=a²+b².

Worked solution

Square the eccentricity relation.
$\frac{c^2}{a^2}=\frac32,\quad b^2=c^2-a^2=\frac{a^2}2$
Substitute the point and solve for positive semiaxes.
$\frac{12}{a^2}-\frac4{a^2/2}=1\implies a^2=4,\ b^2=2$

x²/4−y²/2=1.

Checks and common pitfalls: For a hyperbola c² is a²+b², unlike the corresponding ellipse relation.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Square the eccentricity relation.
$\frac{c^2}{a^2}=\frac32,\quad b^2=c^2-a^2=\frac{a^2}2$
Substitute the point and solve for positive semiaxes.
$\frac{12}{a^2}-\frac4{a^2/2}=1\implies a^2=4,\ b^2=2$

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

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