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Show that the straight lines (A^2-3B^2)x...

Show that the straight lines `(A^2-3B^2)x^2+ 8ABxy + (B^2-3A^2)y^2 = 0` form with the line Ax + By + C = 0 an equilateral triangle whose area is `(C^2)/(sqrt3 (A^2+B^2))`

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Show that the lines (x+2a)^2-3y^2=0,x=a form an equilateral triangle.

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Knowledge Check

  • The area of the triangle formed by the pair of lines 3x^(2) + 8xy - 3y^(2) = 0 and the line 3x + 4y - 5 =0 is,

    A
    `3/5 sq. units`
    B
    `5/3 sq. units`
    C
    `4/5 sq. units`
    D
    `5/4 sq. units`

  • The area of the triangle formed by the pair of lines 3x^(2) + 8xy - 3y^(2) = 0 and the line 3x + 4y - 5 =0 is,

    A
    `3/5 sq. units`
    B
    `5/3 sq. units`
    C
    `4/5 sq. units`
    D
    `5/4 sq. units`

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    Show that the straight lines represented by (x+2a)^(2)-3y^(2)=0 and x=a form an equilateral triangle .

    Show that the straight lines represented by 3x^2+48xy+23y^2=0,3x-2y+13=0 form an equilateral triangle of area (13)/(sqrt(3)) sq. units

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