If p and q are the lengths of perpendiculars from the origin to the lines `xcostheta-ysintheta=kcos2theta` and `xsec""theta+y"c o s e c"""theta=""k` , respectively, prove that `p^2+4q^2=k^2` .

If p and q are the lengths of perpendiculars from the origin to the lines x cos theta-y sin theta=k cos2 theta and x sec theta+y csc theta=k respectively,prove that quad p^(2)+4q^(2)=k^(2)

If p and q are the lengths of perpendicular from the origin to the line x cos(theta)-y sin(theta)=k cos(2 theta) and x sec(theta)+y cos ec(theta)=k respectively,then prove that p^(2)+4q^(2)=k^(2)

If p_(1) and p_(2) are the lengths of the perpendicular form the orgin to the line x sec theta+y cosec theta=a and xcostheta-y sin theta=a cos 2 theta respectively then prove that 4p_(1)^(2)+p_(2)^(2)=a^(2)

If p_1a n d\ p_2 are the lengths of te perpendiculars from the origin upon the lines x\ s e ctheta+h y cos e ctheta=a\ a n d\ xcostheta-ysintheta=acos2theta respectively, then 4p1 2+p2 2=a^2 b. p1 2-4p2 2=a^2 c. p1 2+p2 2=a^2 d. none of these

If p and p_1 be the lengths of the perpendiculars drawn from the origin upon the straight lines x sin theta + y cos theta = 1/2 a sin 2 theta and x cos theta - y sin theta = a cos 2 theta , prove that 4p^2 + p^2_1 = a^2 .

If sin theta + cos theta = p and sec theta + "cosec"theta = q , then prove that q(p^(2)-1) = 2p .

Distance of the lines xcosectheta+ysectheta=kcot2theta and xsintheta+ycostheta=ksin2theta from origin is p and q respectively then

If p\ a n d\ p ' be the perpendicular form the origin upon the straight lines x s e ctheta+y cos e ctheta=a\ a n d\ xcostheta-y s intheta=acos2thetadot Prove that : 4p^2+p^'^2=a^2\ dot