Question

已知圆O：x^2+y^2=a^2,A(-a,o)B(a,0),P1,P2为圆O上关于x轴对称的两点,则直线AP1与BP2

Answer 1

P(x,y)

P1(b,c),P2(b,-c)

k(AP)=c/(a+b)=y/(x+a).(1)

k(BP)=c/(a-b)=y/(x-a).(2)

(1)/(2)

(a-b)/(a+b)=(x-a)/(x+a)

b=a^2/x,c=ay/x

(xP1)^2+(yP1)^2=a^2

(a^2/x)^2+(ay/x)^2=a^2

点P的轨迹方程:x^2-y^2=a^2