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If $p_{1}, p_{2}$ denote the lengths of the perpendiculars from the origin on the lines $x s e c a + y \cos e c a = 2 a$ and $x \cos a + y \sin a = a \cos 2 a$ respectively,

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4sin24α

4cos24α

4 cosec24α

4 sec24α

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detailed solution

Correct option is C

p12+p22=4a2sec2⁡α+cosec2⁡α+a2cos2⁡2αcos2⁡α+sin2⁡α =a2sin2⁡2α+cos2⁡2α=a2and p12p22=a4sin2⁡2αcos2⁡2α=(1/4)a4sin2⁡4α∴p1p2+p2p12=p12+p222p12p22=4sin2⁡4α=4cosec2⁡4α.

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If p1, p2 denote the lengths of the perpendiculars from the origin on the lines xseca+ycoseca=2a and x cos a + y sin a = a cos 2a respectively,

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If $p_{1}, p_{2}$ denote the lengths of the perpendiculars from the origin on the lines $x s e c a + y \cos e c a = 2 a$ and $x \cos a + y \sin a = a \cos 2 a$ respectively,