CBSE Class 11-science Answered
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 | 30 Apr, 2014, 09:08: AM
The perpendicular distance from the origin to the line
x cos q - y sin q = k cos 2 q ... (i)
![](https://images.topperlearning.com/topper/questions/11285_image015.gif)
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](https://images.topperlearning.com/topper/tinymce/cache/a0210d2f9f974191b510fb1d0308ebe9.png)
The perpendicular distance q from the origin to the line (ii)
![](https://images.topperlearning.com/topper/questions/11285_image017.gif)
Answered by | 30 Apr, 2014, 11:08: AM
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