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