tangent of Acute angle between pair of straight lines ax2+2hxy+by2 is given by tanθ=∣∣∣2√h2−aba−b∣∣∣
False
Given equation ax2+2hxy+by2 =0
Let's two equations passing through origin with slope m1 And m2 be
Y=m1 x and y=m2x
Pair of straight line
(m1x-y)(m2x-y)=0
m1m2x2 - (m1 + m2)xy + y2=0
Comparing this equation with given equation
ax2b+2hbxy+y2=0
m1m2=ab m1+m2=−2hb
We know, acute angle between two lines
Tanθ=∣∣m1−m21+m1m2∣∣
We need the value of m1−m2.This can be find out using identity
(m1−m2)2=(m1+m2)2−4m1m2
= (−2hb)2−4ab
= 4h2b2−4ab
(m1−m2)2=4(h2−ab)b2
m1−m2=2√h2−abb
So, tangent of acute angle
tanθ=2√h62−abba+ab=2√h2−aba+b
tanθ=2√h2−aba+b
So, given statement is false because in denominator its given a - b.