LEARN · EXPLAIN · REVISE

Find c².

Read the idea, work independently, then explain what changed.

高二選擇性必修第一册(A版).pdf · 3.2 · PDF 123 / printed page 118

Revisit first: Ellipse

TOPIC 01

Hyperbola

Use the distance-difference definition, asymptotes and branch restrictions.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Foundation#Worked example

x^2/4-y^2/4=1

a,b>0 and e>1; a distance difference is absolute, and an asymptote is not part of the curve.

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Translate the geometric condition into a coordinate equation.

Hint 2

Use this intermediate relation.

c^2=a^2+b^2

Worked solution

The requested value is 8.

Checks and common pitfalls: The focal square is a sum for a hyperbola.

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

Teacher preparation and assessment

Parameters: For x²/a²−y²/b²=1, c²=a²+b² and asymptotes are y=±(b/a)x.
Branch conditions: a,b>0 and e>1; a distance difference is absolute, and an asymptote is not part of the curve.