find the equation or lines which pass through the origin and makes an angle of 45° with the line 3x-y=6
Answers
Answer:
2y=x
Step-by-step explanation:
The equation of any line is written as
Y= mX+C , where M is the slop of that line.
If the line passes through origin the constant (c) is zero
here given that a line passes through origin so the equation of this line must be written as Y=mX
another line is given as 3x-y=6
or y= 3x-6 , so here slop is 3
Now we know that to find the angle between any two line , we calculate this as TanФ= (M2-M1)/(1+M1*M2)
as here angle given is 45° , so Tan45= (M2-M1)/(1+M1*M2)
since Tan45°= 1
so, 1+M1*M2=M2-M1
or put M2 value as 3
1+3*M1= 3-M1
i.e 4*M1= 2
or M1= 1/2
Thus equation of first line be written as Y= M*X
Y= (1/2)*X
2Y=X
Answer:
2y = x
y = -2x
Step-by-step explanation:
Tan (Angle between lines) = | (m₁ - m₂ / (1 + m₁m₂)|
3x-y=6 => y = 3x - 6 => m₁ = 3
Tan 45° = | (3 - m₂)/(1 + 3m₂)|
=> 1 = | (3 - m₂)/(1 + 3m₂)|
case 1 :
(3 - m₂)/(1 + 3m₂) = 1
=> 3 - m₂ = 1 + 3m₂
=> 4m₂ = 2
=> m₂= 1/2
y = x/2 + c
as it passes through origin so c = 0
=> 2y = x
Case 2 :
(3 - m₂)/(1 + 3m₂) = -1
=> 3 - m₂ = -1 - 3m₂
=> 2m₂ = -4
=> m₂= -2
y = -2x