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Prove that the locus of the point of int...

Prove that the locus of the point of intersection of the lines `sqrt(3) x-y-4sqrt(3) k=0 and sqrt(3) kx + ky-4sqrt(3) = 0` for different values of `k` is a hyperbola whose eccentricity is 2.

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The locus of the point of intersection of lines sqrt3x-y-4sqrt(3k) =0 and sqrt3kx+ky-4sqrt3=0 for different value of k is a hyperbola whose eccentricity is 2.

Find the locus of the point of intersection of the lines sqrt(3x)-y-4sqrt(3 lambda)=0 and sqrt(3)lambda x+lambda y-4sqrt(3)=0 for different values of lambda.

Knowledge Check

  • Locus of the point of intersection of the lines mx sqrt(3) + my - 4sqrt(3) = 0 and xsqrt(3) - y - 4 msqrt(3) = 0 , where m is parameter , is

    A
    a parabola
    B
    a hyperbola with e = 2
    C
    an ellipse with ` e = (2)/(3)`
    D
    a circle

  • The locus of the point of intersection of the lines, sqrt(2)x-y+4sqrt(2)k=0" and "sqrt(2)kx+ky-4sqrt(2)=0 (k is any non-zero real parameter), is:

    A
    A hyperbola with length of its transverse axis `8sqrt(2)`
    B
    A hyperbola whose eccentricity is `sqrt(3)`
    C
    An ellipse whose eccentricity is `(1)/(sqrt(3))`
    D
    An ellipse with length of its major axis `8sqrt(2)`

  • The angle between the lines sqrt(3)x-y-2=0 and x-sqrt(3)y+1=0 is

    A
    `90^(@)`
    B
    `60^(@)`
    C
    `45^(@)`
    D
    `30^(@)`

    • Similar Questions

    Explore conceptually related problems

    The locus of the point of intersection of the lines sqrt(3)x-y-4sqrt(3)t=0&sqrt(3)tx+ty-4sqrt(3)=0 (where t is a parameter) is a hyperbola whose eccentricity is:

    The locus of the point of intersection of the lines sqrt(3)x-y-4sqrt(3)lambda=0 and sqrt(3)lambda x+lambda y-4sqrt(3)=0 is a hyperbola of eccentricity 1 b.2 c.3 d.4

    The locus of the point of intersection of the lines (sqrt(3))kx+ky-4sqrt(3)=0 and sqrt(3)x-y-4(sqrt(3))k=0 is a conic, whose eccentricity is ____________.

    (4) sqrt(3)x^(2)+2x-sqrt(3)=0

    sqrt (2x) -sqrt (3y) = 0sqrt (3x) -sqrt (3y) = 0

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