TS ICET 23 May 2019 Shift 1 Paper

Question : 116 of 200

Marks: +1, -0

Two lines

L_1

and

L_2

make intercepts a , - b and b , - a respectively onthe x and y axes. Then angle between

L_1

and

L_2

Solution:

The equation of line

l _{1} ⇒ \;{ x }/{ a }-\;{ y }/{ b }=1

= bx – ay = ab
The equation of line

l_{2} ⇒ \;{x}/{b}-\;{y}/{a}=1

= ax-by = 1

∴ slope of

l_1=b/a

Slope of

l_2=a/b

Angle between two lines

\tan θ=|\;{m_{1}-m_{2}}/{1+m_{1} m_{2}}|=|\;{\;{b}/{a}-{a}/{b}}/{1+(\;{b}/{a})(\;{a}/{b})}|

∴ θ=\tan ^{-1}(\;{b^{2}-a^{2}}/{2 a b})

=\tan ^{-1}(\;{a^{2}-b^{2}}/{2 a b})

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