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 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).

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 .

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

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

If p&q are lengths of perpendicular from the origin x sin alpha+y cos alpha=a sin alpha cos alpha and x cos alpha-y sin alpha=a cos2 alpha, then 4p^(2)+q^(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).

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 & q are lengths of perpendicular from the origin x sin alpha + y cos alpha = a sin alphacos alpha and x cos alpha-y sin alpha = acos 2alpha, then 4p^2 + q^2