椭圆与双曲线类比(急!若M,N是椭圆C:x^2/a^2+y^2/b^2=1(a>b>0)上关于原点对称的两个点,点P是椭圆上任意一点,当直线PM,PN的斜率都存在时,K(pm)*K(pn)是与点P位置无关的定值.试对双曲线x^2/a^2+y^2/b^2
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![椭圆与双曲线类比(急!若M,N是椭圆C:x^2/a^2+y^2/b^2=1(a>b>0)上关于原点对称的两个点,点P是椭圆上任意一点,当直线PM,PN的斜率都存在时,K(pm)*K(pn)是与点P位置无关的定值.试对双曲线x^2/a^2+y^2/b^2](/uploads/image/z/14113069-61-9.jpg?t=%E6%A4%AD%E5%9C%86%E4%B8%8E%E5%8F%8C%E6%9B%B2%E7%BA%BF%E7%B1%BB%E6%AF%94%EF%BC%88%E6%80%A5%21%E8%8B%A5M%2CN%E6%98%AF%E6%A4%AD%E5%9C%86C%EF%BC%9Ax%5E2%2Fa%5E2%2By%5E2%2Fb%5E2%3D1%28a%3Eb%3E0%29%E4%B8%8A%E5%85%B3%E4%BA%8E%E5%8E%9F%E7%82%B9%E5%AF%B9%E7%A7%B0%E7%9A%84%E4%B8%A4%E4%B8%AA%E7%82%B9%2C%E7%82%B9P%E6%98%AF%E6%A4%AD%E5%9C%86%E4%B8%8A%E4%BB%BB%E6%84%8F%E4%B8%80%E7%82%B9%2C%E5%BD%93%E7%9B%B4%E7%BA%BFPM%2CPN%E7%9A%84%E6%96%9C%E7%8E%87%E9%83%BD%E5%AD%98%E5%9C%A8%E6%97%B6%2CK%28pm%29%2AK%EF%BC%88pn%EF%BC%89%E6%98%AF%E4%B8%8E%E7%82%B9P%E4%BD%8D%E7%BD%AE%E6%97%A0%E5%85%B3%E7%9A%84%E5%AE%9A%E5%80%BC.%E8%AF%95%E5%AF%B9%E5%8F%8C%E6%9B%B2%E7%BA%BFx%5E2%2Fa%5E2%2By%5E2%2Fb%5E2)
椭圆与双曲线类比(急!若M,N是椭圆C:x^2/a^2+y^2/b^2=1(a>b>0)上关于原点对称的两个点,点P是椭圆上任意一点,当直线PM,PN的斜率都存在时,K(pm)*K(pn)是与点P位置无关的定值.试对双曲线x^2/a^2+y^2/b^2
椭圆与双曲线类比(急!
若M,N是椭圆C:x^2/a^2+y^2/b^2=1(a>b>0)上关于原点对称的两个点,点P是椭圆上任意一点,当直线PM,PN的斜率都存在时,K(pm)*K(pn)是与点P位置无关的定值.试对双曲线x^2/a^2+y^2/b^2=1(a>b>0)写出具有类似特征的性质,并加以证明.
打掉了。是“试对双曲线x^2/a^2+y^2/b^2=1(a>0,b>0)写出具有类似特征的性质,并加以证明。”
椭圆与双曲线类比(急!若M,N是椭圆C:x^2/a^2+y^2/b^2=1(a>b>0)上关于原点对称的两个点,点P是椭圆上任意一点,当直线PM,PN的斜率都存在时,K(pm)*K(pn)是与点P位置无关的定值.试对双曲线x^2/a^2+y^2/b^2
设M(X0,Y0),N(-X0,-Y0)为双曲线x^2/a^2-y^2/b^2=1(a>0,b>0)的两定点,P(x,y)为其上任意一点,则K(PM)=(y-y0)/(x-x0),K(PN)=(y+y0)/(x+x0),
x^2/a^2-y^2/b^2=1 (1)
x0^2/a^2-y0^2/b^2=1 (2)
(1)-(2)得(x+x0)(x-x0)/a^2=(y+y0)(y-y0)/b^2
从而K(PM)*K(PN)=(y-y0)/(x-x0)*(y+y0)/(x+x0)=b^2/a^2