SATHEE: Straight Line Question 224

Straight Line Question 224

Question: If $ p_1,p_2 $ are the lengths of the normal drawn from the origin on the lines $ x\cos \theta +ysin\theta =2acos4\theta $ And $ x\sec \theta +y\cos ec\theta =4a\cos 2\theta $ respectively, and $ mp^2_1+np^2_2=4a^{2}. $ Then

Options:

A) $ m=1,n=1 $

B) $ m=1,n=4 $

C) $ m=4,n=1 $

D) $ m=1,n=-1 $

Show Answer

Answer:

Correct Answer: B

Solution:

[b] $ p^2_1=4a^{2}{{\cos }^{2}}4\theta $ $ p^2_2=\frac{16a^{2}{{\cos }^{2}}2\theta }{{{\sec }^{2}}\theta +\cos ec^{2}\theta }=16a^{2}{{\cos }^{2}}2\theta {{\cos }^{2}}\theta {{\sin }^{2}}\theta $ $ =a^{2}{{\sin }^{2}}4\theta $

$ \therefore p^2_1+4p^2_2=4a^{2} $

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Straight Line Question 224

Question: If $ p_1,p_2 $ are the lengths of the normal drawn from the origin on the lines $ x\cos \theta +ysin\theta =2acos4\theta $ And $ x\sec \theta +y\cos ec\theta =4a\cos 2\theta $ respectively, and $ mp^2_1+np^2_2=4a^{2}. $ Then

Options:

Answer:

Solution:

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