高中拋物線(xiàn)知識(shí)點(diǎn)歸納總結(jié)與練習(xí)題答案

1、拋物線(xiàn))0(22??ppxy)0(22???ppxy)0(22??ppyx)0(22???ppyx定義平面內(nèi)與一個(gè)定點(diǎn)和一條定直線(xiàn)的距離相等的點(diǎn)的軌跡叫做拋物線(xiàn)，點(diǎn)Fl叫做拋物線(xiàn)的焦點(diǎn)，直線(xiàn)叫做拋物線(xiàn)的準(zhǔn)線(xiàn)。Fl=點(diǎn)M到直線(xiàn)的距離MFMl范圍0xyR??0xyR??0xRy??0xRy??對(duì)稱(chēng)性關(guān)于軸對(duì)稱(chēng)x關(guān)于軸對(duì)稱(chēng)y(0)2p(0)2p?(0)2p(0)2p?焦點(diǎn)焦點(diǎn)在對(duì)稱(chēng)軸上頂點(diǎn)(00)O離心率=1e2px??2px?2py??2p

2、y?準(zhǔn)線(xiàn)方程準(zhǔn)線(xiàn)與焦點(diǎn)位于頂點(diǎn)兩側(cè)且到頂點(diǎn)的距離相等。頂點(diǎn)到準(zhǔn)線(xiàn)的距離2p焦點(diǎn)到準(zhǔn)線(xiàn)的距離p焦半徑焦半徑11()Axy12pAFx??12pAFx???12pAFy??12pAFy???焦點(diǎn)弦點(diǎn)弦長(zhǎng)AB12()xxp??12()xxp???12()yyp??12()yyp???xyOlFxyOlFlFxyOxyOlF，bxxkbkxbkxyy2)(212121????????2212122121)())((bxxkbxxkbkxbkxy

3、y???????在涉及弦長(zhǎng)，中點(diǎn)，對(duì)稱(chēng)，面積等問(wèn)題時(shí)，常用此法，比如1.1.相交弦相交弦ABAB的弦長(zhǎng)的弦長(zhǎng)2122122124)(11xxxxkxxkAB???????ak???21或2122122124)(1111yyyykyykAB???????ak???21b.中點(diǎn)中點(diǎn)，)(00yxM2210xxx??2210yyy??22點(diǎn)差法：點(diǎn)差法：設(shè)交點(diǎn)坐標(biāo)為，，代入拋物線(xiàn)方程，得)(11yxA)(22yxB1212pxy?2222px

4、y?將兩式相減，可得)(2))((212121xxpyyyy????2121212yypxxyy????a.在涉及斜率問(wèn)題時(shí)，在涉及斜率問(wèn)題時(shí)，212yypkAB??b.在涉及中點(diǎn)軌跡問(wèn)題時(shí)在涉及中點(diǎn)軌跡問(wèn)題時(shí)，設(shè)線(xiàn)段的中點(diǎn)為，AB)(00yxM，00212121222ypypyypxxyy??????即，0ypkAB?同理，對(duì)于拋物線(xiàn)，若直線(xiàn)與拋物線(xiàn)相交于兩點(diǎn)，點(diǎn))0(22??ppyxlBA、是弦的中點(diǎn)，則有)(00yxMABpxpx