find the value of K, if the angle between the stright line 4x-Y+7=0and kx-5y-9=0 is 45°
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Answer:
⟹y=4x+7
Therefore, m
1
=4 is the slope of the above equation.
Similarly, for the straight line,
kx−5y−7=0
⟹y=
5
k
x+
5
9
Therefore, m
2
=
5
k
is the slope of the above equation.
The angle two two straight lines is given as:
tanθ=
∣
∣
∣
∣
∣
1+m
1
m
2
m
1
−m
2
∣
∣
∣
∣
∣
Therefore, the angle between the given straight lines is given as
tan45
0
=
∣
∣
∣
∣
∣
∣
∣
∣
1+4×
5
k
4−
5
k
∣
∣
∣
∣
∣
∣
∣
∣
⟹1=
∣
∣
∣
∣
∣
∣
∣
∣
5
5+4k
5
20−k
∣
∣
∣
∣
∣
∣
∣
∣
⟹1=
∣
∣
∣
∣
∣
5+4k
20−k
∣
∣
∣
∣
∣
⟹20−k=5+4k
⟹15=5k
⟹k=3
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