Q. 104.0( 4 Votes )
If p1 and p2 are the lengths of the perpendiculars form the origin upon the lines x sec θ + y cosec θ = a and x cos θ – y sin θ = a cos 2 θ respectively, then
A. 4p12 + p22 = a2
B. p12 + 4p22 = a2
C. p12 + p22 = a2
D. none of these
Answer :
The given lines are
x sec θ + y cosec θ = a … (1)
x cos θ − y sin θ = a cos 2 θ … (2)
p1 and p2 are the perpendiculars from the origin upon the lines (1) and (2), respectively.
⇒ 4p12 + p22 = a2 (sin2 2θ + cos2 2 θ) = a2
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