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Question

If (a+3b)(3a+b)=4h2then the angle between the lines represented by ax2+2hxy+by2=0 is


A

300

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B

450

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C

600

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D

tan-1(½)

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Solution

The correct option is C

600


The explanation for the correct option:

Finding the angle:

Given (a+3b)(3a+b)=4h2

3a2+9ab+ab+3b2=4h23a2+10ab+3b2=4h2..(i)

We know the angle between pair of straight lines ax2+2hxy+by2=0

tanθ=2(h2ab)(a+b)=(4h24ab)(a+b)=(3a2+10ab+3b24ab)(a+b)------(from(i))=(3a2+6ab+3b2)(a+b)=3(a2+2ab+b2)(a+b)=3(a+b)2(a+b)=3(a+b)(a+b)=3

θ=tan-1(3)=600

Hence, option (C) is the correct answer.


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