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If tangents be drawn from points on the line `x=c` to the parabola `y^2=4x`, show that the locus of point of intersection of the corresponding normals is the parabola.

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The locus of points of intersection of perpendicular tangents to a parabola is a

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Knowledge Check

  • Tangents are drawn at the end points of a normal chord of the parabola y^(2)=4ax . The locus of their point of intersection is

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

  • Perpendicular tangents are drawn from an external point P to the parabola y^2=16(x-3) Then the locus of point P is

    A
    `x=1`
    B
    `x=-1`
    C
    `x=1/2`
    D
    `x=2`

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    If two tangents drawn from a point P on the parabola y^2 = 4x are at right angles, then the locus of P is

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    The ordinates of points P and Q on the parabola y^2=12x are in the ration 1:2 . Find the locus of the point of intersection of the normals to the parabola at P and Q.

    The locus of the point of intersection of the perpendicular tangents to the parabola x^(2)-8x+2y+2=0 is

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