LEARN · EXPLAIN · REVISE

Find the length of the focal chord perpendicular to the axis.

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

高二選擇性必修第一册(A版).pdf · 3.3 · PDF 135 / printed page 130

Revisit first: Hyperbola

TOPIC 01

Parabola

Relate focus, directrix and vertex, and retain conditions in line-parabola intersections.

Relate focus, directrix and vertex, and retain conditions in line-parabola intersections.
Justify the method and check the conditions in a new situation.

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

01 / Standard#Your turn

y^2=40x

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.

x=a\Rightarrow y^2=4a^2

Worked solution

Translate the geometric condition into a coordinate equation.
Apply the stated relation and retain its conditions.
$y=\pm2(10)\Rightarrow L=40$
The latus rectum has length 4|a|.

The requested value is 40.

Checks and common pitfalls: The latus rectum has length 4|a|.

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

Teacher preparation and assessment

Relate focus, directrix and vertex, and retain conditions in line-parabola intersections.
Which condition is essential in parabola?
How does changing the sign of a alter y²=4ax?

Focus-directrix: y²=4ax has focus (a,0) and directrix x=−a.
Nondegeneracy: a must be nonzero; a parabola has a vertex and no center of symmetry.