已知A(1,0),椭圆c:x^2/4+y^2/3=1,过点A做直线交椭圆c于P,Q两点,AP=2QA,则直线PQ的斜率

已知A(1,0),椭圆c:x^2/4+y^2/3=1,过点A做直线交椭圆c于P,Q两点,AP=2QA,则直线PQ的斜率
已知A(1,0),椭圆c:x^2/4+y^2/3=1,过点A做直线交椭圆c于P,Q两点,AP=2QA,则直线PQ的斜率

已知A(1,0),椭圆c:x^2/4+y^2/3=1,过点A做直线交椭圆c于P,Q两点,AP=2QA,则直线PQ的斜率
C:x^2/4+y^2/3=1,A(1,0)
设直线PQ:x=ty+1代入x^2/4+y^2/3=1,
(ty+1)²/4+y²/3=1
即(3t²+4)y²+6ty-9=0
设P(x1,y1),Q(x2,y2)
∴y1+y2=-6t/(3t²+4),
y1y2=-9/(3t²+4)
∵AP=2QA
∴y1=-2y2
那么
-y2=-6t/(3t²+4)
- y²2=-9/(3t²+4)
消去y2得：
36t²/(3t²+4)²=9/(3t²+4)
∴4t²=3t²+4
∴t²=4,t=±2
∴直线PQ的斜率为1/t=±1/2