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Parabola

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Similar Questions

Explore conceptually related problems

A fixed parabola y^(2) = 4ax touches a variable parabola. Find the equation to the locus of the vertex of the variable parabola. Assume that the two parabolas are equal and the axis of the variable parabola remains parallel to the xaxis.

The endpoints of two normal chords of a parabola are concyclic.Then the tangents at the feet of the normals will intersect (a) at tangent at vertex of the parabola (b) axis of the parabola (c) directrix of the parabola (d) none of these

Knowledge Check

  • Observe the following facts for a parabola. (i) Axis of the parabola is the only line which can be the perpendicular bisector of the two chords of the parabola. (ii) If AB and CD are two parallel chords of the parabola and the normals at A and B intersect at P and the normals at C and D intersect at Q, then PQ is a normal to the parabola. The directrix of the parabola is

    A
    `y-1/24=0`
    B
    `y+1/24=0`
    C
    `y+1/12=0`
    D
    `y-1/12=0`

  • Consider a point P on a parabola such that 2 of the normal drawn from it to the parabola are at right angles on parabola, then If P -= (x _(1), y _(1)), the slope of third normal is, if If the equation of parabola is y^(2)= 8x

    A
    `(y _(1))/(8)`
    B
    `(y _(1))/(2)`
    C
    `-(y _(1))/(8)`
    D
    `- (y _(1))/(2)`

  • Consider a point P on a parabola such that 2 of the normal drawn from it to the parabola are at night angles on parabola, then The ratio of latus rectum of given parabola and that of made by locus of point P is

    A
    `4:1`
    B
    `2:1`
    C
    `16:1`
    D
    `1:1`

    • Similar Questions

    Explore conceptually related problems

    Consider two parabola y=x^(2)-x+1 and y=x^(2)+x+(1)/(2), the parabola y=-x^(2)+x+(1)/(2) is fixed and parabola y=-x^(2)+1 rolls without slipping around the fixed parabola,then the locus of the focus of the moving parabola is

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