A) \[\frac{2a\cos \theta }{{{\sin }^{2}}\theta }\]
B) \[\frac{4a\cos \theta }{{{\sin }^{2}}\theta }\]
C) \[\frac{4a\cos \theta }{3{{\sin }^{2}}\theta }\]
D) None of the above
Correct Answer: A
Solution :
Let any point \[(h,\,\,k)\] will satisfy \[{{y}^{2}}=4ax\] \[i.e.,\] \[{{k}^{2}}=4ah\] ... (i) Let a line \[OP\] makes an angle \[\theta \] from the axis. \[\therefore \] In\[\Delta OAP,\,\,\sin \theta =\frac{PA}{OP}\] \[\Rightarrow \] \[\sin \theta =\frac{k}{l}\] \[\Rightarrow \] \[k=l\sin \theta \] and \[\cos \theta =\frac{OA}{OP}\] \[\Rightarrow \] \[\cos \theta =\frac{h}{l}\] From Eq. (i), we get \[{{l}^{2}}{{\sin }^{2}}\theta =4a\times l\cos \theta \] (put\[k=l\sin \theta ,\,\,h=l\cos \theta )\] \[\Rightarrow \] \[l=\frac{4a\cos \theta }{{{\sin }^{2}}\theta }\]You need to login to perform this action.
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