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If the pole of the normal at P lie on th...

If the pole of the normal at P lie on the normal at Q, then show that the pole of the normal at Q lies on the normal at P.

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Normality

P(t_(1)) and Q(t_(2)) are the point t_(1) and t_(2) on the parabola y^(2)=4ax. The normals at P and Q meet on the parabola.Show that the middle point PQ lies on the parabola y^(2)=2a(x+2a)

If the normal at P(18, 12) to the parabola y^(2)=8x cuts it again at Q, then the equation of the normal at point Q on the parabola y^(2)=8x is

Normal at P(t1) cuts the parabola at Q(t2) then relation

Knowledge Check

  • A point P moves such that sum of the slopes of the normals drawn from it to the hyperbola xy=16 is equal to the sum of the ordinates of the feet of the normals. Let 'P' lies on the curve C, then : Q. The equation of 'C' is :

    A
    `x^(2)=4y`
    B
    `x^(2)=16y`
    C
    `x^(2)=12y`
    D
    `y^(2)=8x`

  • If the normal at P(18, 12) to the parabola y^(2)=8x cuts it again at Q, then the equation of the normal at point Q on the parabola y^(2)=8x is

    A
    `27y=99x-2058`
    B
    `27y=99x+3058`
    C
    `27y=-99x-3058`
    D
    None of these

  • A point P moves such that sum of the slopes of the normals drawn from it to the hyperbola xy=16 is equal to the sum of the ordinates of the feet of the normals. Let 'P' lies on the curve C, then : Q. If tangents are drawn to the curve C, then the locus of the midpoint of the portion of tangent intercepted between the co-ordinate axes, is :

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