1.

Let OP = r and angle XOP = theta then the position of P in polar coordinate system is represented by (r,theta) OX and O are called the initial line and pole respectively. If p be the length of perpendicular from origin to line and if alpha is the angle which the perpendicular to the line makes with the initial line . The equation of line is given by r cos (theta - alpha) = p The polar coordinates of the foot of perpendicular from the pole on the line joining the two points (r_1,theta_1 ) and (r_2,theta_2) are

Answer»

`[(r_1r_2sin(theta_2-theta_1))/(SQRT(r_1^2+r_2^2-2r_1r_2cos(theta_1-theta_2))),TAN^(-1)((r_1costheta_1-r_2costheta_2)/(r_2sintheta_2-r_1sintheta_2))]`
`[(r_1r_2sin(theta_2+theta_1))/(sqrt(r_1^2+r_2^2-2r_1r_2cos(theta_1-theta_2))),tan^(-1)((r_1costheta_1-r_2costheta_2)/(r_2sintheta_2-r_1sintheta_1))]`
`[(-r_1r_2sin(theta_2-theta_1))/(sqrt(r_1^2+r_2^2-2r_1r_2cos(theta_1-theta_2))),tan^(-1)((r_1costheta_1-r_2costheta_2)/(r_2sintheta_2-r_1sintheta_1))]`
NONE of these

Answer :A


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