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Find the combined equation of the lines ...

Find the combined equation of the lines through the origin :
(1) each making an ange of `45^(@)` with the line `3x + y = 2.`
(2) each making an angle of `pi//6` with the line `3x + y - 6 = 0` .
(3) which form an equilateral triangle with the line `3x + 4y = 8.`

Text Solution

AI Generated Solution

To solve the problem of finding the combined equations of lines through the origin for the given conditions, we will break it down into three parts as specified in the question. ### Part 1: Lines making an angle of 45 degrees with the line \(3x + y = 2\) 1. **Find the slope of the given line:** The equation of the line is \(3x + y = 2\). Rearranging it to slope-intercept form: \[ y = -3x + 2 ...
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Find the equation of the lines through the point (3,2) which make an angle of 45^(@) with the line x-2y=3

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Knowledge Check

  • Joint equation of two lines through the origin, each making angle of 45^(@) with line 3x-y=0 is

    A
    `2x^(2)-3xy-2y^(2)=0`
    B
    `2x^(2)+3xy+4y^(2)=0`
    C
    `2x^(2)+3xy-2y^(2)=0`
    D
    `3x^(2)+2xy-3y^(2)=0`

  • The joint equation of pair of lines passing through the origin and making an angle of 45^(@) with the line 3x+y=0 is

    A
    `x^(2)+3xy+y^(2)=0`
    B
    `2x^(2)+3xy+y^(2)=0`
    C
    `2x^(2)+3xy-2y^(2)=0`
    D
    `3x^(2)+2xy-2y^(2)=0`

  • Joint equation of two lines through the origin each making angle of 30^(@) with line x+y=0 , is

    A
    `x^(2)-4xy+y^(2)=0`
    B
    `x^(2)+4xy+y^(2)=0`
    C
    `x^(2)-4xy-y^(2)=0`
    D
    `x^(2)+4xy-y^(2)=0`

    • Similar Questions

    Explore conceptually related problems

    Find the joint equation of the pair of the lines through the origin each of which is making an angle of 30^(@) with the line 3x+2y-11=0 .

    Find the joint equation of the pair of lines through the origin and making an equilateral triangle with the line x = 3.

    Joint equation of two lines through the origin each making angle of 60^(@) with line x-y=0 , is

    The joint equation of pair of lines through the origin and making an angle of (pi)/(6) with the line 3x+y-6=0 is

    The equation of the lines passes through (2,3) and making an angle of 45^(@) with the line 2x-y+3=0 is

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