Q. 505.0( 1 Vote )
If p and q are the lengths of perpendiculars from the origin to the lines xcosθ -ysinθ =kcos2θ and xsecθ +ycosθ =k, respectively, prove that p2+4q2=k2
Answer :
Given lines are xcosθ -ysinθ = -kcos2θ
And xsecθ +ycosecθ =k
Now, we find perpendicular of these lines from the origin
P = and q=
P=kcos2θ and q = kcosθ sinθ
P=kcos2θ and q =
Cos2θ = , q=
i.e. sin2θ =
Since cos22θ +sin22θ =1
We have,
Or p2+4q2=k2
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