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Question

tangent of Acute angle between pair of straight lines ax2+2hxy+by2 is given by tanθ=2h2abab


A

True

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B

False

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Solution

The correct option is 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=m1m21+m1m2

We need the value of m1m2.This can be find out using identity

(m1m2)2=(m1+m2)24m1m2

= (2hb)24ab

= 4h2b24ab

(m1m2)2=4(h2ab)b2

m1m2=2h2abb

So, tangent of acute angle

tanθ=2h62abba+ab=2h2aba+b

tanθ=2h2aba+b

So, given statement is false because in denominator its given a - b.


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