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`

If p\ and\ q be the perpendicular form the origin upon the straight lines x s e ctheta+ycosectheta=a\ and\ xcostheta-y sintheta=acos2theta Prove that : 4p^2+q^2=a^2\ dot

If p and q are the prependicular distance from the origin to the straight lines xsectheta-ycosectheta=a and xcostheta+ysin theta =acos2theta then

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_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 a.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' be perpendiculars from the origin upon the straight lines x sec theta+y"cosec"theta=a and x cos theta-y sin theta=a cos 2theta , then the value of the expression 4p^(2)+p'^(2) is :

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 p_(1) " and " p_(2) are the lengths of the perpendiculars from the origin to the straight lines xsectheta+ycosectheta=2a " and " xcostheta-ysintheta=acos2theta , then prove that p_(1)""^(2)+p_(2)""^(2)=a^(2) .

If p and q are respectively the perpendiculars from the origin upon the straight lines, whose equations are x sec theta + y cosec theta =a and x cos theta -y sin theta = acos 2 theta , then 4p^(2) + q^(2) is equal to