高中數(shù)學(xué)第2章圓錐曲線與方程2.2.2橢圓的幾何性質(zhì)9省公開課一等獎(jiǎng)新名師獲獎(jiǎng)?wù)n件

橢圓幾何性質(zhì)（1）

1/68一、復(fù)習(xí)回顧：平面內(nèi)到兩定點(diǎn)F1、F2距離之和為常數(shù)（大于|F1F2|）動(dòng)點(diǎn)軌跡叫做橢圓②、焦點(diǎn)在x軸上橢圓標(biāo)準(zhǔn)方程為

，焦點(diǎn)坐標(biāo)為

焦點(diǎn)在y軸上橢圓標(biāo)準(zhǔn)方程為

，焦點(diǎn)坐標(biāo)為

①、橢圓定義:2/68二、問題導(dǎo)學(xué)：①、函數(shù)有最大值還是最小值？為何？②、橢圓和橢圓圖象為何如前一節(jié)橢圓標(biāo)準(zhǔn)方程書本28頁2-2-1和29頁2-2-2所表示？你前面想過這個(gè)問題嗎？③、圖像為何不是向左右或上下無限延伸呢？你能經(jīng)過對(duì)橢圓方程研究找到解釋嗎？3/681、范圍：即由和由-a≤x≤a,-b≤y≤b圖像在矩形框內(nèi)，但到底是什么形狀？你能大致畫出來嗎？yoxx=-ay=-bx=a4/68①、稱為橢圓頂點(diǎn)：A1(－a，0)，A2(a，0)，B1(0，－b)，B2(0，b).oxyA2(a,0)A1(-a,0)B2(0,b)B1(0,-b)（a＞b＞0）②、長軸：線段A1A2；長軸長|A1A2|=2a.③、短軸：線段B1B2；短軸長|B1B2|=2b.a和b分別叫做橢圓長半軸長和短半軸長；注意2、頂點(diǎn)：5/68

3、對(duì)稱性：（a＞b＞0）①、從圖形上看：

橢圓既是以x軸，y軸為對(duì)稱軸軸對(duì)稱圖形，又是以坐標(biāo)原點(diǎn)為對(duì)稱中心中心對(duì)稱圖形。6/68yxoF1F2··x2y2＋=1a22b橢圓對(duì)稱性動(dòng)畫展示：7/68yxoF1F2··x2y2＋=1a22b8/68yxoF1F2··x2y2＋=1a22b9/68yxoF1F2··x2y2＋=1a22b10/68yxoF1F2··x2y2＋=1a22b11/68yxoF1F2··x2y2＋=1a22b12/68yxoF1F2··x2y2＋=1a22b13/68yxoF1F2··x2y2＋=1a22b14/68yxoF1F2··x2y2＋=1a22b15/68yxoF1F2··x2y2＋=1a22b16/68yxoF1F2··x2y2＋=1a22b17/68yxoF1F2··x2y2＋=1a22b18/68yxoF1F2··x2y2＋=1a22b19/68yxoF1F2··x2y2＋=1a22b20/68yxoF1F2··x2y2＋=1a22b21/68yxoF1F2··x2y2＋=1a22b22/68yxoF1F2··x2y2＋=1a22b23/68yxoF1F2··x2y2＋=1a22b24/68yxoF1F2··x2y2＋=1a22b25/68yxoF1F2··x2y2＋=1a22b26/68yxoF1F2··x2y2＋=1a22b27/68yxoF1F2··x2y2＋=1a22b28/68yxoF1F2··x2y2＋=1a22b29/68yxoF1F2··x2y2＋=1a22b30/68yxoF1F2··x2y2＋=1a22b31/68yxoF1F2··x2y2＋=1a22b32/68yxoF1F2··x2y2＋=1a22b33/68yxoF1F2··x2y2＋=1a22b34/68yxoF1F2··x2y2＋=1a22b35/68yxoF1F2··x2y2＋=1a22b36/68yxoF1F2··x2y2＋=1a22b37/68yxoF1F2··x2y2＋=1a22b38/68yxoF1F2··x2y2＋=1a22b39/68yxoF1F2··x2y2＋=1a22b40/68yxoF1F2··x2y2＋=1a22b41/68yxoF1F2··x2y2＋=1a22b42/68yxoF1F2··x2y2＋=1a22b43/68yxoF1F2··x2y2＋=1a22b44/68yxoF1F2··x2y2＋=1a22b45/68yxoF1F2··x2y2＋=1a22b46/68yxoF1F2··x2y2＋=1a22b47/68yxoF1F2··x2y2＋=1a22b48/68yxoF1F2··x2y2＋=1a22b49/68yxoF1F2··x2y2＋=1a22b50/68yxoF1F2··x2y2＋=1a22b51/68yxoF1F2··x2y2＋=1a22b52/68yxoF1F2··x2y2＋=1a22b53/68yxoF1F2··x2y2＋=1a22b54/68yxoF1F2··x2y2＋=1a22b55/68yxoF1F2··x2y2＋=1a22b56/68yxoF1F2··x2y2＋=1a22b57/68yxoF1F2··x2y2＋=1a22b58/68YXOP（x，y）P2（-x，y）P3（-x，-y）P1（x，-y）關(guān)于x軸對(duì)稱關(guān)于y軸對(duì)稱關(guān)于原點(diǎn)對(duì)稱②、從作對(duì)稱點(diǎn)角度看：59/68（1）把x換成-x，方程（2）把y換成-y，方程不變，圖象關(guān)于x軸對(duì)稱；（3）把x換成-x，同時(shí)把y換成-y方程不變，圖象關(guān)于原點(diǎn)成中心對(duì)稱。

③、從方程角度看：歸納：橢圓關(guān)于X軸對(duì)稱、關(guān)于Y軸對(duì)稱、關(guān)于原點(diǎn)對(duì)稱，原點(diǎn)稱為橢圓對(duì)稱中心。不變，圖象關(guān)于y軸對(duì)稱；60/68oxyB2(0,b)B1(0,-b)A2(a,0)A1(-a,0)bacF2F1問題導(dǎo)學(xué)：④、你能利用尺軌準(zhǔn)確作出橢圓兩個(gè)焦點(diǎn)嗎？

⑤、求？（用a,b,c表示）

⑥、當(dāng)b不變，a增大時(shí)變大還是變小？為何？

兩種方法？⑦、變大，橢圓形狀發(fā)生了怎樣改變？61/68oxybacF2F14、離心率：（反應(yīng)橢圓扁平程度）注：①、離心率越大橢圓越扁；離心率越小橢圓越圓；②、離心率范圍？

③、特征三角形62/68標(biāo)準(zhǔn)方程圖象范圍對(duì)稱性頂點(diǎn)坐標(biāo)焦點(diǎn)坐標(biāo)半軸長焦距a,b,c關(guān)系離心率|x|≤a,|y|≤b|x|≤b,|y|≤a關(guān)于x軸、y軸成軸對(duì)稱；關(guān)于原點(diǎn)成中心對(duì)稱。（a,0）,(0,b)（b,0）,(0,a)(±c,0)(0,±c)長半軸長為a,短半軸長為b.焦距為2c;a2=b2+c263/68合作探討：例1：求橢圓長軸和短軸長、離心率、焦點(diǎn)和頂點(diǎn)坐標(biāo)，并大致畫出這個(gè)橢圓圖像64/68合作探討：例題2：與

圖像更靠近圓（填前者或后者）65/68課堂小結(jié)：你認(rèn)為本節(jié)課要掌握哪些