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 `cdot` Prove that the locus of their middle point is the curve. `(y^2-4a x)(ycosalpha+2asinalpha)^2+a^2c^2=0.`

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 family of chords of the parabola y^2=4ax is drawn so that their projections on a straight line inclined equally to both the axes are all of a constant length c, prove that the locus of their middle points is the curve (y^2-4ax)(y+2a)^2+2a^2c^2=0 .

The locus of the middle points of the focal chords of the parabola,y^(2)=4x is:

The locus of the middle points of the focal chord of the parabola y^(2)=4ax , is

A pair of tangents are drawn to the parabola y^(2)=4ax which are equally inclined to a straight line y=mx+c, whose inclination to the axis is alpha. Prove that the locus of their point of intersection is the straight line y=(x-a)tan2 alpha.

The locus of the middle points of normal chords of the parabola y^(2)=4ax is-