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

Explanation

We have,
p1​= Length of the perpendicular from (0,0) to xsectheta+ycosectheta=a

⇒`p1​=(​acosthetasintheta​)/sqrt(sin^2theta+cos^2theta)`



`p1=asinthetacostheta`

⇒`2p1​=2asinthetacostheta`

⇒`2p1​=asin2theta`

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