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Find the separate equations of the lines...

Find the separate equations of the lines represented by :
(1) `3x^(2) -7xy + 4y^(2) = 0`
(2) `6x^(2) - 5xy - 6y^(2) = 0`
(3) `2x^(2) + 2xy - y^(2) = 0`
(4) `x^(2) - y^(2) + x + y = 0.`

Text Solution

Verified by Experts

(1) `x -y = 0, 3x -4y = 0`
(2) `2x - 3y = 0, 3x + 2y = 0`
(3) `(1+sqrt(3)) x -y = 0, (1-sqrt(3)) x -y = 0`
(4) `x + y = 0, x - y + 1 = 0` .
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Knowledge Check

  • The equation of the lines represented by 3x^(2)-7xy+4y^(2)=0 are

    A
    `x+2y=0 and 3x+2y=0`
    B
    `3x-y=0 and x-4y=0`
    C
    `x-2y=0 and 3x-2y=0`
    D
    `x-y=0 and 3x-4y=0`
  • The equation of the lines represented by 6x^(2)-5xy-6y^(2)=0 are

    A
    `2x+3y=0 and 3x+2y=0`
    B
    `2x-3y=0 and 3x-2y=0`
    C
    `2x-3y=0 and 3x+2y=0`
    D
    `2x+3y=0 and 3x-2y=0`
  • Separate eqation of lines represented by the equation 6x^2+5xy-4y^2=0 is

    A
    `x-2y=0 and x+3y=0`
    B
    `2x-y=0 and 3x+4y=0`
    C
    `x+y=0 and x-4y=0`
    D
    `2x^2+y^2-xy+11x-y+12=0`
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