双曲线的标准方程公式
双曲线的标准方程公式:焦点在X轴上时为：x²/a²-y²/b²=1(a>0,b>0)；焦点在Y轴上时为：y²/a²-x²/b²=1(a>0,b>0)。双曲线是指与平面上到两个定点的距离之差的绝对值为定值的点的轨迹，也可以定义为到定点与定直线的距离之比是一个大于1的常数的点之轨迹。绛旓細鍙屾洸绾跨殑鏍囧噯鏂圭▼涓簒^2/a^2 - y^2/b^2 = 1鍜寉^2/b^2 - x^2/a^2 = 1銆傚叾涓紝a鍜宐鏄父鏁颁笖a銆乥鍧囦笉绛変簬闆躲傝繖涓や釜鏂圭▼鍒嗗埆鎻忚堪浜嗗弻鏇茬嚎鍦ㄧ洿瑙掑潗鏍囩郴涓殑褰㈡併傛í鍙屾洸绾夸互x杞翠负瀵圭О杞达紝绾靛弻鏇茬嚎浠杞翠负瀵圭О杞淬傝繖涓や釜鏂圭▼閮借〃绀轰簡涓庝袱鏉＄洿绾胯窛绂荤浉绛夌殑鐐圭殑杞ㄨ抗褰㈡垚鍙屾洸绾跨殑鎯呭喌...
绛旓細鍙屾洸绾x^2/a^2-y^2/b^2=1鐨勫噯绾鐨勬柟绋灏辨槸x=鍦焌^2/c锛堣涓篶鍒嗕箣a鏂癸級,y^2/a^2-x^2/b^2=1鐨勫噯绾挎柟绋嬫槸Y=鍦焌^2/c, 鍏朵腑a鏄疄鍗婅酱闀匡紝b鏄櫄鍗婅酱闀匡紝c鏄崐鐒﹁窛銆傦紙c^2 = a^2 + b^2 锛変緥濡傦紝瀛樺湪鍙屾洸绾縳^2/9-y^2/4=1 鎸夌収浠ヤ笂璁＄畻鍏紡锛屽垯鍏跺噯绾挎柟绋嬩负 L1鐨...
绛旓細鍙屾洸绾跨殑鍩烘湰鐭ヨ瘑鐐鍏紡锛氬弻鏇茬嚎鏍囧噯鏂圭▼ 瀵逛簬骞抽潰涓婄殑鍙屾洸绾匡紝鏍囧噯鏂圭▼涓簒^2/a^2 - y^2/b^2 = 1銆傚弻鏇茬嚎鏄袱鏉″叿鏈夊叡鍚岀劍鐐圭殑瀵圭О鏇茬嚎锛屽叾鍩烘湰鐗规у寘鎷腑蹇冦佺劍鐐广侀《鐐圭瓑銆傚湪鏂圭▼涓紝x杞翠负瀹炶酱锛寉杞翠负铏氳酱锛岃繖涓や釜杞寸殑閫夋嫨鍩轰簬鍏蜂綋鐨勬儏鍐点傛牴鎹洸绾跨殑鐗规у彲浠ョ‘瀹氶《鐐逛綅缃拰绂诲績鐜囩瓑閲嶈鍙傛暟...
绛旓細鍙傛暟鏂圭▼濡備笅锛氫竴銆佸渾鐨勫弬鏁版柟绋媥=a+rcos胃锛寉=b+rsin胃锛埼糕垐[0锛2蟺)锛夛紝(a,b)涓哄渾蹇冨潗鏍囷紝r涓哄渾鍗婂緞锛屛镐负鍙傛暟锛(x,y)涓虹粡杩囩偣鐨勫潗鏍囥備簩銆佹き鍦嗙殑鍙傛暟鏂圭▼x=acos胃锛寉=bsin胃锛埼糕垐[0锛2蟺锛夛級a涓洪暱鍗婅酱闀縝涓虹煭鍗婅酱闀课镐负鍙傛暟銆備笁銆鍙屾洸绾跨殑鍙傛暟鏂圭▼x=asec胃锛堟鍓诧級锛寉=b...
绛旓細鍙屾洸绾匡紙Hyperbola锛夌殑鏍囧噯鏂圭▼锛氬弻鏇茬嚎鏄钩闈笂鍒颁袱涓畾鐐笷1鍜孎2鐨勮窛绂讳箣宸瓑浜庡父鏁2a鐨勭偣鐨勮建杩广鍙屾洸绾跨殑鏍囧噯鏂圭▼鏈変袱绉嶅舰寮忥細a) 姘村钩鏂瑰悜鐨勫弻鏇茬嚎锛(x^2 / a^2) - (y^2 / b^2) = 1鍏朵腑锛宎鍜宐鍒嗗埆鏄弻鏇茬嚎鐨勪袱涓崐杞寸殑闀垮害锛孎1鍜孎2鏄弻鏇茬嚎鐨勪袱涓劍鐐广俠) 鍨傜洿鏂瑰悜鐨勫弻鏇茬嚎锛(y^...
绛旓細褰撶劍鐐瑰湪x杞存椂锛屾き鍦嗙殑鏍囧噯鏂圭▼鏄細x^2/a^2+y^2/b^2=1锛(a>b>0)锛涘綋鐒︾偣鍦▂杞存椂锛屾き鍦嗙殑鏍囧噯鏂圭▼鏄細y^2/a^2+x^2/b^2=1锛(a>b>0)锛涘叾涓璦^2-c^2=b^2銆傛帹瀵:PF1+PF2>F1F2(P涓烘き鍦嗕笂鐨勭偣 F涓虹劍鐐)銆鍙屾洸绾跨殑鏍囧噯鏂圭▼鍒嗕袱绉嶆儏鍐碉細鐒︾偣鍦╔杞翠笂鏃朵负锛歺^2/a^2-y^2/...
绛旓細鍦鍙屾洸绾跨殑鏍囧噯鏂圭▼涓紝a銆乥銆乧浠ｈ〃涓嶅悓鐨勫弬鏁帮紝瀹冧滑鍒嗗埆瀵瑰簲浜庡弻鏇茬嚎鐨勫悇涓壒寰併傚浜庢按骞虫柟鍚戠殑鍙屾洸绾匡紙宸﹀彸寮鍙ｏ級锛屾爣鍑嗘柟绋嬩负锛(x²/a²) - (y²/b²) = 1 - 鍙傛暟a锛氬畾涔夊弻鏇茬嚎鍦▁杞翠笂鐨勫绉颁腑蹇冪偣鐨勬í鍧愭爣銆- 鍙傛暟b锛氬畾涔夊弻鏇茬嚎鍦▂杞翠笂鐨勫绉颁腑蹇冪偣鐨勭旱鍧愭爣銆-...
绛旓細c鏄崐鐒﹁窛銆備緥濡傦紝瀛樺湪鍙屾洸绾縳^2/9-y^2/4=1 鎸夌収浠ヤ笂璁＄畻鍏紡锛屽垯鍏跺噯绾鏂圭▼涓 L1鐨勬柟绋嬶細x=-a^2/c=-9/鈭13, L2鐨勬柟绋嬶細x=a^2/c=9/鈭13銆傚彟澶栵紝鎸夌収鍙屾洸绾跨劍鐐规墍鍦ㄨ酱绾夸笉鍚岋紝鍙屾洸绾跨殑鍑嗙嚎鏂圭▼涔熸湁鍋氱浉搴旇皟鏁淬傚浜庢爣鍑嗙殑浠ュ師鐐逛负涓績锛岀劍鐐逛綅浜嶺杞存垨Y杞鐨勬爣鍑鍙屾洸绾裤
绛旓細鍙屾洸绾跨涓夊畾涔夋枩鐜囦箣绉粙缁嶅涓嬶細鍙屾洸绾跨涓夊畾涔夋槸骞抽潰鍐呯殑鍔ㄧ偣鍒颁袱瀹氱偣A1(a锛0)銆丄2(-a锛0)鐨勬枩鐜囦箻绉瓑浜庡父鏁癳^2-1鐨勭偣鐨勮建杩瑰彨鍋氭き鍦嗘垨鍙屾洸绾裤鍙屾洸绾挎柟绋嬪叕寮浠嬬粛濡備笅锛鏍囧噯鏂圭▼1锛氱劍鐐瑰湪X杞翠笂鏃朵负x2/a2-y2/b2=1(a>0锛宐>0)銆傛爣鍑嗘柟绋1锛氱劍鐐瑰湪Y杞翠笂鏃朵负y2/a2-x2/b2=1(a>0...
绛旓細鍙屾洸绾跨殑鍩烘湰鐭ヨ瘑鐐鍏紡鏄細1銆佸弻鏇茬嚎鐨勫畾涔夊強鏍囧噯鏂圭▼锛氱洿绾夸笌鍙屾洸绾夸氦浜庝竴鐐规椂锛屼笉涓瀹氱浉鍒囷紝渚嬪锛氬綋鐩寸嚎涓庡弻鏇茬嚎鐨勬笎杩戠嚎骞宠鏃讹紝鐩寸嚎涓庡弻鏇茬嚎鐩镐氦浜庝竴鐐癸紝浣嗕笉鏄浉鍒囷紱鍙嶄箣锛屽綋鐩寸嚎涓庡弻鏇茬嚎鐩稿垏鏃讹紝鐩寸嚎涓庡弻鏇茬嚎浠呮湁涓涓氦鐐广2銆佸簲鐢ㄥ弻鏇茬嚎鐨勫畾涔夐渶娉ㄦ剰鐨勯棶棰橈細鍦ㄥ弻鏇茬嚎鐨勫畾涔変腑瑕佹敞鎰忓弻鏇茬嚎涓婄殑...
