عنقود مرايا كقطوع مكافئة - بؤرة، دليل وما بينهما - جزء ت

2 مسألة هدف 2 – تلخيص

أكملوا الجدول التالي، وجدوا العلاقة بين التعبير الجبري للقطع المكافئ الملائم لمرآة قطع مكافئ (باربوليت) وبين بؤرتها.
لأجل ذلك نختار نقطة على القطع المكافئ (B).

(يمكن الضغط على الرسم وتكبيرها)

تعبير جبري للقطع المكافئ	إحداثيات نقطة $B$ على القطع المكافئ	إحداثيات البؤرة $(F)$
$p(x)=0.25x^2$	$(1,0.25)$
$p(x)=x^2$	$(1,1)$
$p(x)=2x^2$	$(1,2)$
$p(x)=4x^2$	$(1,4)$
$p(x)=ax^2$	$(1,a)$

كلما كانت المرآة على شكل القطع المكافئ أوسع، هل تكون البؤرة أقرب إلى رأس القطع المكافئ أم أبعد عنه؟ علّلوا إجابتكم.

إذا حليّتم مسألة هدف 2، انتقلوا إلى ماذا يمكن أن نسأل أيضًا.

اختاروا إحداثي x للنقطة $B$ :
بواسطة جرّ النقطة $B$ على القطع المكافئ، أو بواسطة شريط الجر $x(B)$ .
غيّروا قيم شريط الجر a ، وافحصوا تأثير قيمة a على مكان البؤرة ( $F$ ) والدليل (الخط $m$ ).

مبنى العنقود

1. مسألة هدف 1
- 1.1 درجة 1
- 1.2 درجة 2
2. مسألة هدف 2
3. ماذا يمكن أن نسأل أيضًا؟

מאו”פ מתמטי

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