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 p^{2} + 4q^{2} = k^{2}.

### 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)

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Now,

x sec q + y cosec q = k

The perpendicular distance q from the origin to the line (ii)

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

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