Straight Lines and Pair of Straight Lines Part 1

Given, the equation of median through B i.e. BE:2x+y−3=0
Equation, of angle bisector of C i.e. CD:7x−4y=1
Since, E satisfies the equation of BE.
∴ 2(

a−3

2

)+(

b+1

2

)−3=0
2a−6+b+1−6=0
2a+b=11 ...(i)
Since, C satisfies CD.
7a−4b=1 ...(ii)
On solving Eqs. (i) and (ii), we get
a=3,b=5
Slope of AC=

2

3

Slope of CD=

7

4

∴tan(

θ

2

)=|

2 3 − 7 4

1+ 14 12

|=

1

2

Now, tan‌θ=

2‌tan( θ 2 )

1−tan2( θ 2 )

=

2. 1 2

1− 1 4

=

4

3