已知椭圆C的离心率为根号3除以2在x轴上顶点为a1(-2,0),a2(2,0)1求椭圆的方程

3个回答

  • 1.a=2,c=a*e=2*√3/2=√3,b=√(4-3)=1,则椭圆方程为:x^2/4+y^2=1

    2.设P(t,y0),PA1方程:y=y0/(t+2)*(x+2),PA2方程:y=y0/(t-2)*(x-2),

    PA1方程与椭圆方程联立,解得x1=-2,x2=(-8y0+2(t+2)^2)/(4y0^2+(t+2)^2),

    Y1=0,y2=4(t+2)y0/(4y0^2+(t+2)^2),即M(x2,y2)

    PA2方程与椭圆方程联立,解得x3=2,x4=(8y0-2(t+2)^2)/(4y0^2+(t+2)^2),

    y3=0,y4=-4(t-2)y0/(4y0^2+(t+2)^2),即N(x4,y4)

    MN直线方程整理得:y=2ty0*x/((t+2)^2-4y0)+8y0/(4y0^2+(t+2)^2),

    椭圆焦点F1(√3,0)或F2(-√3,0)代入上式,左端≠右端,所以,直线MN不通过椭圆的焦点.