双曲线的渐近线教案.docx
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双曲线的渐近线教案.docx
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双曲线的渐近线教案
双曲线的渐近线教案
教学目的
(1)正确理解双曲线的渐近线的定义,能利用双曲线的渐近线来画双曲线的图形(
(2)掌握由双曲线求其渐近线和由渐近线求双曲线的方法,并能作初步的应用,从而提高分析问题和解决问题的能力(
教学过程
一、揭示课题
师:
给出双曲线的方程,我们能把双曲线画出来吗,
生(众):
能画出来(
师:
能画得比较精确点吗,
(学生默然()
其附近的点,比较精确地画出来(但双曲线向何处伸展就不很清楚了(在画其他曲线时,也有同样的问题(如曲线
我们可以比较精确地画出整个曲线(因为我们知道,当曲线伸向远处时,它逐渐地越
ofleadership,alongwith500-1000punishment.(5)significantnearmissshouldbeattemptedasthecaseofresponsiblefortheaccidentandconstructionteaminjuriesaccidentpenaltyprovisions,mutatismutandis.Eight,shouldperformintheconstructionstandardsandspecifications,serialnumbera1GB3323-2005steelfusionweldedbuttjoints,weldingengineering-Raylightingandqualityratingof2GB11345-89steelweldsmanualmethodsofultrasonicinspectionandtestingresultsforgrade3GB50236-2002industrialpipeweldingengineeringcodeforconstructionandacceptanceoffieldequipment4HGJ222-92technicalspecificationforweldingofaluminiumanditsalloys5lowtemperaturesteelweldingprocedure6SH3525-2004petrochemicalJB/T4708-2000ofweldingprocedurequalificationforsteelpressurevessels7JB/4709-20008JB4730-2005pressurevesselweldingproceduresofsteelpressurevesselNDT9JB/T4744-2000steelpressurevesselproductsmechanicalpropertiestestofweldedplateII,mechanicalequipmentinstallationengineering1GB150-982GB50128-2005verticalcylindricalsteelpressurevesselsteelweldedspecificationforconstructionandacceptanceofoiltank3JB/T4735-1997steelweldedatmosphericpressurevessel4GB50231-2009mechanicalequipmentinstallationengineeringconstructionandacceptancespecificationfor5GB50275-98compressor,fanandpumpinstallationengineeringconstructionandacceptancespecificationforlifting6HG20201-2000constructioninstallationengineeringconstructionstandard7,HG...Pressuregauges,usinganinstalledsparkarrestorforacetylenecylinders,illegalcarrying,usinggascylinders,eachoperatorfined20Yuan.Gasbottlewithoutthehot
的趋向,我们是清楚的,它逐渐地在x轴负方向上越来越接近x轴,即x轴为y,2x的一条渐近线,但它的另一端则不然,它伸向何处是不够清楚的(所以双曲线和其他曲线一样,当它向远处伸展时,它的趋向如何,是需要研究的问题(今天这堂课,我们就来讨论一下“双曲线向何处去”这样一个问题(
(板书课题:
双曲线的渐近线()
二、讲述定义
师:
前一课我们讨论了双曲线的范围、对称性和顶点,我们回忆一下,双曲线的范围x?
a,x?
a是怎样得出来的,
直线x,,a和x,a的外侧(我们能不能把双曲线的范围再缩小一点,我们先看看双曲线在第一象限的情况(
设M(x,y)是双曲线上在第一象限内的点,则
考察一下y变化的范围:
222因为x,a,x,所以
这个不等式意味着什么,
(稍停,学生思考()
ofleadership,alongwith500-1000punishment.(5)significantnearmissshouldbeattemptedasthecaseofresponsiblefortheaccidentandconstructionteaminjuriesaccidentpenaltyprovisions,mutatismutandis.Eight,shouldperformintheconstructionstandardsandspecifications,serialnumbera1GB3323-2005steelfusionweldedbuttjoints,weldingengineering-Raylightingandqualityratingof2GB11345-89steelweldsmanualmethodsofultrasonicinspectionandtestingresultsforgrade3GB50236-2002industrialpipeweldingengineeringcodeforconstructionandacceptanceoffieldequipment4HGJ222-92technicalspecificationforweldingofaluminiumanditsalloys5lowtemperaturesteelweldingprocedure6SH3525-2004petrochemicalJB/T4708-2000ofweldingprocedurequalificationforsteelpressurevessels7JB/4709-20008JB4730-2005pressurevesselweldingproceduresofsteelpressurevesselNDT9JB/T4744-2000steelpressurevesselproductsmechanicalpropertiestestofweldedplateII,mechanicalequipmentinstallationengineering1GB150-982GB50128-2005verticalcylindricalsteelpressurevesselsteelweldedspecificationforconstructionandacceptanceofoiltank3JB/T4735-1997steelweldedatmosphericpressurevessel4GB50231-2009mechanicalequipmentinstallationengineeringconstructionandacceptancespecificationfor5GB50275-98compressor,fanandpumpinstallationengineeringconstructionandacceptancespecificationforlifting6HG20201-2000constructioninstallationengineeringconstructionstandard7,HG...Pressuregauges,usinganinstalledsparkarrestorforacetylenecylinders,illegalcarrying,usinggascylinders,eachoperatorfined20Yuan.Gasbottlewithoutthehot
平面区域(
之间(含x轴部分)(这样,我们就进一步缩小了双曲线所在区域的范围(
为此,我们考虑下列问题:
经过A、A作y轴的平行线x,?
a,经过B、B作x轴的平行线y2121
?
b,
以看出,双曲线
的各支向外延伸时,与这两条直线逐渐接近(
ofleadership,alongwith500-1000punishment.(5)significantnearmissshouldbeattemptedasthecaseofresponsiblefortheaccidentandconstructionteaminjuriesaccidentpenaltyprovisions,mutatismutandis.Eight,shouldperformintheconstructionstandardsandspecifications,serialnumbera1GB3323-2005steelfusionweldedbuttjoints,weldingengineering-Raylightingandqualityratingof2GB11345-89steelweldsmanualmethodsofultrasonicinspectionandtestingresultsforgrade3GB50236-2002industrialpipeweldingengineeringcodeforconstructionandacceptanceoffieldequipment4HGJ222-92technicalspecificationforweldingofaluminiumanditsalloys5lowtemperaturesteelweldingprocedure6SH3525-2004petrochemicalJB/T4708-2000ofweldingprocedurequalificationforsteelpressurevessels7JB/4709-20008JB4730-2005pressurevesselweldingproceduresofsteelpressurevesselNDT9JB/T4744-2000steelpressurevesselproductsmechanicalpropertiestestofweldedplateII,mechanicalequipmentinstallationengineering1GB150-982GB50128-2005verticalcylindricalsteelpressurevesselsteelweldedspecificationforconstructionandacceptanceofoiltank3JB/T4735-1997steelweldedatmosphericpressurevessel4GB50231-2009mechanicalequipmentinstallationengineeringconstructionandacceptancespecificationfor5GB50275-98compressor,fanandpumpinstallationengineeringconstructionandacceptancespecificationforlifting6HG20201-2000constructioninstallationengineeringconstructionstandard7,HG...Pressuregauges,usinganinstalledsparkarrestorforacetylenecylinders,illegalcarrying,usinggascylinders,eachoperatorfined20Yuan.Gasbottlewithoutthehot
下面,我们来证明这个事实(
双曲线在第一象限内的方程可写成
设M(x,y)是它上面的点,N(x,Y)是直线
上与M有相同横坐标的点,则
设|MQ|是点M到直线
的距离,则|MQ|,|MN|(当x逐渐增大时,|MN|逐渐减小,x无限增大,|MN|接近于零,|MQ|也接近于零,就是说,双曲线在第一象限的部分从射线ON的下方逐渐接近于射线ON(
在其他象限内也可以证明类似的情况(我们把两条直线
叫做双曲线的渐近线(
ofleadership,alongwith500-1000punishment.(5)significantnearmissshouldbeattemptedasthecaseofresponsiblefortheaccidentandconstructionteaminjuriesaccidentpenaltyprovisions,mutatismutandis.Eight,shouldperformintheconstructionstandardsandspecifications,serialnumbera1GB3323-2005steelfusionweldedbuttjoints,weldingengineering-Raylightingandqualityratingof2GB11345-89steelweldsmanualmethodsofultrasonicinspectionandtestingresultsforgrade3GB50236-2002industrialpipeweldingengineeringcodeforconstructionandacceptanceoffieldequipment4HGJ222-92technicalspecificationforweldingofaluminiumanditsalloys5lowtemperaturesteelweldingprocedure6SH3525-2004petrochemicalJB/T4708-2000ofweldingprocedurequalificationforsteelpressurevessels7JB/4709-20008JB4730-2005pressurevesselweldingproceduresofsteelpressurevesselNDT9JB/T4744-2000steelpressurevesselproductsmechanicalpropertiestestofweldedplateII,mechanicalequipmentinstallationengineering1GB150-982GB50128-2005verticalcylindricalsteelpressurevesselsteelweldedspecificationforconstructionandacceptanceofoiltank3JB/T4735-1997steelweldedatmosphericpressurevessel4GB50231-2009mechanicalequipmentinstallationengineeringconstructionandacceptancespecificationfor5GB50275-98compressor,fanandpumpinstallationengineeringconstructionandacceptancespecificationforlifting6HG20201-2000constructioninstallationengineeringconstructionstandard7,HG...Pressuregauges,usinganinstalledsparkarrestorforacetylenecylinders,illegalcarrying,usinggascylinders,eachoperatorfined20Yuan.Gasbottlewithoutthehot
现在来看看实轴在y轴上的双曲线的渐近线方程是怎样的,由于实轴在y轴上的双曲线方程是由实轴在x轴上的双曲线方程,将x、y字母对调所得到,自然,前者
这样,我们就完满地解决了画双曲线远处趋向的问题,从而可比较精确地画出双
手画出比较精确的双曲线(
[提出问题,解决问题,善始善终(]
三、初步练习
(根据由双曲线求出它的渐近线方程与由渐近线求出相应的双曲线方程这两要求,出四个小题让学生练习()
1(求下列双曲线的渐近线方程(写成直线方程的一般式),并画出双曲线:
ofleadership,alongwith500-1000punishment.(5)significantnearmissshouldbeattemptedasthecaseofresponsiblefortheaccidentandconstructionteaminjuriesaccidentpenaltyprovisions,mutatismutandis.Eight,shouldperformintheconstructionstandardsandspecifications,serialnumbera1GB3323-2005steelfusionweldedbuttjoints,weldingengineering-Raylightingandqualityratingof2GB11345-89steelweldsmanualmethodsofultrasonicinspectionandtestingresultsforgrade3GB50236-2002industrialpipeweldingengineeringcodeforconstructionandacceptanceoffieldequipment4HGJ222-92technicalspecificationforweldingofaluminiumanditsalloys5lowtemperaturesteelweldingprocedure6SH3525-2004petrochemicalJB/T4708-2000ofweldingprocedurequalificationforsteelpressurevessels7JB/4709-20008JB4730-2005pressurevesselweldingproceduresofsteelpressurevesselNDT9JB/T4744-2000steelpressurevesselproductsmechanicalpropertiestestofweldedplateII,mechanicalequipmentinstallationengineering1GB150-982GB50128-2005verticalcylindricalsteelpressurevesselsteelweldedspecificationforconstructionandacceptanceofoiltank3JB/T4735-1997steelweldedatmosphericpressurevessel4GB50231-2009mechanicalequipmentinstallationengineeringconstructionandacceptancespecificationfor5GB50275-98compressor,fanandpumpinstallationengineeringconstructionandacceptancespecificationforlifting6HG20201-2000constructioninstallationengineeringconstructionstandard7,HG...Pressuregauges,usinganinstalledsparkarrestorforacetylenecylinders,illegalcarrying,usinggascylinders,eachoperatorfined20Yua
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