The perpendicular from the origin to the line joining the points `A(a cos alpha, a sin alpha)` and `B(a sin beta, a cos beta)` divides AB in the ratio

Perpendicular from the origin to the line joining the points (c cos alpha,c sin alpha) and (c cos beta,c sin beta) divides it in the ratio

Perpendicular from the origin to the line joining the points (c cos alpha,c sin alpha) and (c cos beta,c sin beta) divides it in the ratio

The perpendicular form the origin on the line joining the points P(r cos alpha,r sin alpha) and Q(r cos beta,r sin beta) divides PQ in the ratio 1 : k then principal value of cos^(-1)((1)/(k))

Coordinates of the foot of the perpendicular drawn from 0,0 to he line jolning (a cos alpha,a sin alpha) and (a cos beta,a sin beta) are

The locus of the point (r cos alpha cos beta, r cos alpha sin beta, r sin alpha) is

2 sin ^(2) beta + 4 cos (alpha + beta) sin alpha sin beta + cos 2 (alpha + beta )=