Question

已知椭圆的中点在原点,焦点在x轴,短轴长为6离心率为4/5（1）求椭圆标准方程（2）p.p1.p2为椭圆上任意三点,且线

Answer 1

（1）b=3,c/a=4/5,c=4a/5,

b^2=a^2-c^2=(9/25)a^2=9,a^2=25,

椭圆方程是x^2/25+y^2/9=1.

设P(x,y),P1(x1,y1),则P2(-x1,-y1),

x^2/25+y^2/9=1.

x1^2/25+y1^2/9=1.

相减得(x2-x1^2)/25+(y^2-y1^2)/9=0,

(y^2-y1^2)/(x^2-x1^2)=-9/25,

k1=(y-y1)/(x-x1）,k2=(y+y1)/(x+x1),

∴k1*k2=(y^2-y1^2)/(x^2-x1^2)=-9/25.