[" If "p" and "p'" are the lengths of perpendiculars drawn from the origin upon the lines "x" sec "alpha+y],[cosec alpha-a=0" and "x cos alpha-y sin alpha-a cos2 alpha=0," prove that "4p^(2)+p^(prime2)=a^(2)]

If p and p^' are the length of perpendicular drawn from the origin upon the lines xsecalpha + ycosecalpha = 0 and xcosalpha - ysinalpha - acos2alpha = 0 Prove that , 4p^2 + p^('2) = a^2

If p and q are the lengths of the perpendiculars from the origin to the straight lines x sec alpha+y cosec alpha=a and x cos alpha-y sin alpha=a cos 2alpha, prove that 4p^(2)+q^(2)=a^(2)

If P_(1) and p_(2) are the lenghts of the perpendiculars drawn from the origin to the two lines x sec alpha +y . Cosec alpha =2a and x. cos alpha +y. sin alpha =a. cos 2 alpha , show that P_(1)^(2)+P_(2)^(2) is constant for all values of alpha .

If p and q are the lengths of the perpendiculars from the origin to the straight lines x "sec" alpha + y " cosec" alpha = a " and " x "cos" alpha-y " sin" alpha = a "cos" 2alpha, " then prove that 4p^(2) + q^(2) = a^(2).

The perpendicular distance from origin to the line x/(p sec alpha)+y/(p cosec alpha)=1 is

The length of the perpendicular from the origin on the line (x sin alpha)/(b ) - (y cos alpha)/(a )-1=0 is

If p and p' are the distances of the origin from the lines x "sec" alpha + y " cosec" alpha = k " and " x "cos" alpha-y " sin" alpha = k "cos" 2alpha, " then prove that 4p^(2) + p'^(2) = k^(2).

If p and p' are the distances of the origin from the lines x "sec" alpha + y " cosec" alpha = k " and " x "cos" alpha-y " sin" alpha = k "cos" 2alpha, " then prove that 4p^(2) + p'^(2) = k^(2).