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Find the major-axis length.

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

TOPIC 01

Conic sections: mixed review

A mixed assessment: identify the method, justify it and revise your reasoning.

What you will be able to explain

  • Connect the chapter skills without relying on the order of the exercises.

Try it. Leave your reasoning visible.

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

01 / Foundation#Your turn

Find the major-axis length.

x2/484+y2/400=1x^2/484+y^2/400=1
  • For a horizontal major axis a>b>0; the larger denominator specifies the major axis.
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.
major axis=2a\text{major axis}=2a
Worked solution
  1. Translate the geometric condition into a coordinate equation.

  2. Apply the stated relation and retain its conditions.

    2a=2(22)=442a=2(22)=44
  3. An axis is twice the corresponding semiaxis.

The requested value is 44.

Checks and common pitfalls: An axis is twice the corresponding semiaxis.

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

Focus on one question

Teacher preparation and assessment

Question sequence

  • Ask students to name the relevant condition before calculating.

Board plan

  • Compare valid methods and annotate their conditions.

Anticipated thinking

  • A correct final value may still hide a missing assumption.

Assessment checklist

  • Check the method, conditions, reasoning and interpretation separately.

No sign-in. Work stays in this browser. Export before clearing browser data. Written reasoning is assessed with a checklist.

Curriculum and source notes ↗