If p and q are the lengths of perpendicular from the origin to the lines x cos q - y sin q = k cos 2 q and x sec q + y cosec q = k respectively. Prove that p2 + 4q2 = k2.

Asked by Topperlearning User | 30th Apr, 2014, 09:08: AM

Expert Answer:

The perpendicular distance from the origin to the line

x cos q - y sin q = k cos 2 q                                                   ... (i)

Now,
x sec q + y cosec q = k

fraction numerator x over denominator cos theta end fraction plus fraction numerator y over denominator sin theta end fraction equals k

rightwards double arrow x sin theta plus y cos theta equals k sin theta cos theta

rightwards double arrow x sin theta plus y cos theta equals k over 2 sin 2 theta
 
The perpendicular distance q from the origin to the line (ii)

Answered by  | 30th Apr, 2014, 11:08: AM