A line & passes through (0,5)and(-5,0). what is the accute angle between the y-axis and the line in radian measure
Answers
Answer:
Step-by-step explanation:
Let the line which passes through origin and make an angle π/4 with the line x−y+1=0
is AB
Let slope of line AB=m
2
Let slope of line CD(x−y+1=0)=m
1
=1
It is given that the angle between AB and CD is 45
o
tanθ=
∣
∣
∣
∣
∣
1+m
1
m
2
m
1
+m
2
∣
∣
∣
∣
∣
tan45
o
=
∣
∣
∣
∣
∣
1+m
2
1−m
2
∣
∣
∣
∣
∣
±1=(
1+m
2
1−m
2
)
1=
1+m
2
1−m
2
,−1=(
1+m
2
1−m
2
)
1+m
2
=1−m
2
−(1+m
2
)=(1−m
2
)
2m
2
=0 −1−m
2
=1−−m
2
m
2
=0 −2=0 (not possible)
∴ m
2
=0
∴ Equation of line (y−y
1
)=m(x−x
1
)
⇒(y−0)=0(x−0)
y=0
To find: Point of intersection of the line with the given line
Put y=0 in the given line equation
x−0+1=0
x=−1
∴ Point of intersection is (−1,0)Let the line which passes through origin and make an angle π/4 with the line x−y+1=0
is AB
Let slope of line AB=m
2
Let slope of line CD(x−y+1=0)=m
1
=1
It is given that the angle between AB and CD is 45
o
tanθ=
∣
∣
∣
∣
∣
1+m
1
m
2
m
1
+m
2
∣
∣
∣
∣
∣
tan45
o
=
∣
∣
∣
∣
∣
1+m
2
1−m
2
∣
∣
∣
∣
∣
±1=(
1+m
2
1−m
2
)
1=
1+m
2
1−m
2
,−1=(
1+m
2
1−m
2
)
1+m
2
=1−m
2
−(1+m
2
)=(1−m
2
)
2m
2
=0 −1−m
2
=1−−m
2
m
2
=0 −2=0 (not possible)
∴ m
2
=0
∴ Equation of line (y−y
1
)=m(x−x
1
)
⇒(y−0)=0(x−0)
y=0
To find: Point of intersection of the line with the given line
Put y=0 in the given line equation
x−0+1=0
x=−1
∴ Point of intersection is (−1,0)