Any line through P(−1,2) is
where r1,r2,r3 are respectively the distance of the points A,Q and B from the given point P(−1,2).
Point A is (r1cosθ−1,r1sinθ+2)
as the point A lies on x−axis.
Point B is (r3cosθ−1,r3sinθ+2)
as the point B lies on y−axis
Let the point Q be (h,k).
We have to find the locus of the point Q.
Also it is given that r1,r2,r3 are in H.P.
∴2r2=1r1+1r3=−sinθ2+cosθ, by (1)and (2)
or 2r2=−12(k−2)r2+(h+1)r2, by (3)
or k=2h or y=2x