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The chord of the parabola y^2 = 4ax whos...

The chord of the parabola `y^2 = 4ax` whose equation is `y-xsqrt2+ 4asqrt2=0` is a normal to it and its length is `6sqrt3a`.

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The chord of the parabola y^(2)=4ax, whose equation is y-x sqrt(2)+4a sqrt(2)=0, is a normal to the curve,and its length is sqrt(3)a then find lambda.

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Knowledge Check

  • The length of the chord of the parabola y^(2)=4ax whose equation is y-x sqrt2+4asqrt2=0 is

    A
    `2sqrt11a`
    B
    `4sqrt2a`
    C
    `8sqrt2a`
    D
    `6sqrt3a`

  • The length of the chord of the parabola x^(2) = 4y having equations x - sqrt(2) y + 4 sqrt(2) = 0 is

    A
    `8 sqrt(2)`
    B
    `2 sqrt(11)`
    C
    `3 sqrt(2)`
    D
    `6 sqrt(3)`

  • The normal chord of the parabola y^2 = 4ax at a point whose ordinate is equal to abscissą subtends a right angle at the

    A
    focus
    B
    vertex
    C
    ends of latus rectum
    D
    none

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    The normals to the parabola y^(2)=4ax from the point (5a,2a) is/are

    An equilateral triangle is inscribed in the parabola y^2 = 4ax whose vertex is at the vertex of the parabola. The length of its side is

    If the normal chord of the parabola y^(2)=4 x makes an angle 45^(@) with the axis of the parabola, then its length, is

    The locus of the poles of focal chords of the parabola y^2 = 4ax is

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