Question

Find the values of k if the angle between straight lines kx+y+9=0 and 3x-y+4=0 is pi/4

Answer 1

Answer:ANSWER

kx+y+9=0

y=−kx−9

Thus, slope of the line m  

1

​  

=−k

Similarly, y=3x+4

Slope of the line is m  

2

​  

=3

Therefore, angle between the lines is

tanθ=  

∣

∣

∣

∣

∣

​  

 

1+m  

1

​  

m  

2

​  

 

m  

2

​  

−m  

1

​  

 

​  

 

∣

∣

∣

∣

∣

​  

 

=  

∣

∣

∣

∣

∣

​  

 

1−3k

3+k

​  

 

∣

∣

∣

∣

∣

​  

 

=  

∣

∣

∣

∣

∣

​  

 

1−3k

k+3

​  

 

∣

∣

∣

∣

∣

​  

 

But θ=45  

o

 

 

∴tanθ=1

⇒  

1−3k

k+3

​  

=±1

⇒k+3=±(1−3k)

Case I

k+3=1−3k

i.e. 4k=−2

⇒k=  

2

−1

​  

 

Case II

k+3=−1+3k

⇒−2k=−4

∴k=2

Hence, k=2,  

2

−1

​  

Step-by-step explanation: