A family of chords of the parabola y^2=4ax is drawn so that their projections on a straight line...

A series of chords is drawn to the parabola y^(2)=4ax, so that their projections on a straight line which is inclined at an angle alpha to the axis are all of constant length 'c!.If the locus of their middle point is the curve.(y^(2)-lambda ax)(y cos alpha+2a sin alpha)^(2)+a^(2)c^(2)=0. then find lambda.

A series of chords is drawn to the parabola y^(2)=4ax, so that their projections on a straight line which is inclined at an angle alpha to the axis are all of constant length 'c!.If the locus of their middle point is the curve (y^(2)-lambda ax)(y cos alpha+2a sin alpha)^(2)+a^(2)c^(2)=0. Then find lambda

A set of parallel chords of the parabola y^(2)=4ax have their midpoint on any straight line through the vertex any straight line through the focus a straight line parallel to the axis another parabola

A series of chords are drawn so that their projections on the straight line,which is inclined at an angle a to the axis,are of constant length c. Prove that the locus of their middle point is the curve.(y^(2)-4ax)(y cos alpha+2a sin alpha)^(2)+a^(2)c^(2)=0

Circles are described on the chords of the parabola y^(2)=4ax drawn though the vertex.The locus of the centres of circle

Let PQ be a focal chord of the parabola y^(2)=4ax The tangents to the parabola at P and Q meet at a point lying on the line y=2x+a,a>0. Length of chord PQ is

Let PQ be a focal chord of the parabola y^(2)=4ax . The tangents to the parabola at P and Q meet at point lying on the line y=2x+a,alt0 . If chord PQ subtends an angle theta at the vertex of y^(2)=4ax , then tantheta=

If x-2y-a=0 is a chord of the parabola y^(2)=4ax , then its langth, is

If the equation of a chord of the parabola y^(2)=4ax is y=mx+c , then its mid point is