过双曲线x^2/a^2-y^2/b^2=1(a>0,b>0)的左焦点F(-c,0)(c>0),作圆x^2+y^2=a^2/4的切线,切点为E,延长FE延长FE交曲线右支于点P,若向量OE=1/2(向量OF+向量OP),则双曲线的离心率为?设→焦点为F'(c,0),连接PF'∵向量OE
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![过双曲线x^2/a^2-y^2/b^2=1(a>0,b>0)的左焦点F(-c,0)(c>0),作圆x^2+y^2=a^2/4的切线,切点为E,延长FE延长FE交曲线右支于点P,若向量OE=1/2(向量OF+向量OP),则双曲线的离心率为?设→焦点为F'(c,0),连接PF'∵向量OE](/uploads/image/z/2588211-27-1.jpg?t=%E8%BF%87%E5%8F%8C%E6%9B%B2%E7%BA%BFx%5E2%2Fa%5E2-y%5E2%2Fb%5E2%3D1%28a%3E0%2Cb%3E0%29%E7%9A%84%E5%B7%A6%E7%84%A6%E7%82%B9F%EF%BC%88-c%2C0%29%28c%3E0%29%2C%E4%BD%9C%E5%9C%86x%5E2%2By%5E2%3Da%5E2%2F4%E7%9A%84%E5%88%87%E7%BA%BF%2C%E5%88%87%E7%82%B9%E4%B8%BAE%2C%E5%BB%B6%E9%95%BFFE%E5%BB%B6%E9%95%BFFE%E4%BA%A4%E6%9B%B2%E7%BA%BF%E5%8F%B3%E6%94%AF%E4%BA%8E%E7%82%B9P%2C%E8%8B%A5%E5%90%91%E9%87%8FOE%3D1%2F2%28%E5%90%91%E9%87%8FOF%2B%E5%90%91%E9%87%8FOP%29%2C%E5%88%99%E5%8F%8C%E6%9B%B2%E7%BA%BF%E7%9A%84%E7%A6%BB%E5%BF%83%E7%8E%87%E4%B8%BA%3F%E8%AE%BE%E2%86%92%E7%84%A6%E7%82%B9%E4%B8%BAF%27%28c%2C0%29%2C%E8%BF%9E%E6%8E%A5PF%27%E2%88%B5%E5%90%91%E9%87%8FOE)
过双曲线x^2/a^2-y^2/b^2=1(a>0,b>0)的左焦点F(-c,0)(c>0),作圆x^2+y^2=a^2/4的切线,切点为E,延长FE延长FE交曲线右支于点P,若向量OE=1/2(向量OF+向量OP),则双曲线的离心率为?设→焦点为F'(c,0),连接PF'∵向量OE
过双曲线x^2/a^2-y^2/b^2=1(a>0,b>0)的左焦点F(-c,0)(c>0),作圆x^2+y^2=a^2/4的切线,切点为E,延长FE
延长FE交曲线右支于点P,若向量OE=1/2(向量OF+向量OP),则双曲线的离心率为?
设→焦点为F'(c,0),连接PF'
∵向量OE=1/2(向量OF+向量OP)
∴OE垂直平分FP
∴OF=OP
∵OF=OF'
∴OF=OP=OF'
∴△PFF'为直角三角形即FP⊥F'P
∵OE⊥PF
∴F'P=2OE=a
∴FP=F'P+2a=3a
∴在直角三角形PFF'中,PF^2+PF'^2=FF'^2
∴(3a)^2+a^2=(2c)^2
∴e=根号10/2
为什么∵OE⊥PF
∴F'P=2OE=a
∴FP=F'P+2a=3a
求指导,
过双曲线x^2/a^2-y^2/b^2=1(a>0,b>0)的左焦点F(-c,0)(c>0),作圆x^2+y^2=a^2/4的切线,切点为E,延长FE延长FE交曲线右支于点P,若向量OE=1/2(向量OF+向量OP),则双曲线的离心率为?设→焦点为F'(c,0),连接PF'∵向量OE
由△PFF'为直角三角形即FP⊥F'P,且OE垂直平分FP即OE⊥FP,O是FF'的中点,故OE是△PFF'的中位线,即F'P=2OE=2Xa/2=a,再有双曲线定义,FP-F'P=2a,即FP=F'P+2a=3a,
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