question_answer

If p and q are respectively the perpendiculars from the origin upon the straight lines, whose equations are \[x\,\sec \theta +y\,\,\cos ec\theta =a\] and\[x\cos \theta -y\,\,\sin \theta =a\,\,\cos 2\theta \], then \[4{{p}^{2}}+{{q}^{2}}\] is equal to _________.

A)  \[{{a}^{2}}\] 

B)  \[2{{a}^{2}}\]

C)  \[3{{a}^{2}}\]                                   

D)  \[4{{a}^{2}}\]

E)  None of these