If (a+3b)(3a+b)=4h2then the angle between the lines represented by ax2+2hxy+by2=0 is
300
450
600
tan-1(½)
The explanation for the correct option:
Finding the angle:
Given (a+3b)(3a+b)=4h2
⇒3a2+9ab+ab+3b2=4h2⇒3a2+10ab+3b2=4h2..(i)
We know the angle between pair of straight lines ax2+2hxy+by2=0
tanθ=2(h2–ab)(a+b)=(4h2–4ab)(a+b)=(3a2+10ab+3b2–4ab)(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.
If (a + 3b)(3a + b) = 4h2, then the angle between the lines represented by ax2+2hxy+by2=0 is
If the pair of straight lines given by Ax2+2Hxy+By2=0,(H2>AB) forms an equilateral triangle with line ax + by + c = 0, then (A + 3B)(3A + B) is