Prove that the locus of the middle points of all tangents drawn from points on the directrix to the parabola is
`y^(2) (2x+a) =a (3x+a)^(2)`

Prove that the locus of the middle points of all chords of the parabola y^(2)=4ax passing through the vertex is the parabola y^(2)=2ax

Find the locus of the middle points of the chords of contact of orthogonal tangents of the parabola y^(2)=4ax .

Find the number of tangents drawn from the point (-1999 ,-2020) to the parabola y^(2)=x^2+x+1

Find the locus of points of intersection of tangents drawn at the end of all normal chords to the parabola y^2 = 8(x-1) .

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

The locus of the middle point of the chord of contact of tangents drawn from points lying on the straight line 4x-5y=20 to the circle x^(2)+y^(2)=9is

Find the locus of the middle points of the chords of the parabola y^(2) = 4x which touch the parabola x^(2) = -8y .

Angle between the tangents drawn from the point (0 2020) to the parabola (y-2)^(2)=(x-1)