A series of chords is drawn to the parab...

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)` `(ycosalpha+2asinalpha)^2+a^2c^2=0`.then find `lambda`.

Similar Questions

Explore conceptually related problems

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 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 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

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 .

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-

Similar Questions

Recommended Questions