If the distance of the point `(alpha,2)` from its chord of contact w.r.t. the parabola `y^2=4x` is 4, then find the value of `alphadot`

Find the locus of point whose chord of contact w.r.t. to the parabola y^(2) = 4bx is the tangent of the parabola y^(2) = 4ax .

From a point on the axis of x common tangents are drawn to the parabola y^(2)=4x and the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1(agtbgt0) . If these tangents from an equilateral trianlge with their chord of contact w.r.t parabola, then set of exhaustive values of a is

Point of contact of the line kx+y-4=0 w.r.t the parabola y=x-x^2

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

If the chord of contact of tangents from a point P to the parabola y^(2)=4ax touches the parabola x^(2)=4by, then find the locus of P.

Length of the chord of contact drawn from the point (-3,2) to the parabola y^(2)=4x is

If the tangent at the point P(2,4) to the parabola y^(2)=8x meets the parabola y^(2)=8x+5 at Q and R, then find the midpoint of chord QR.

If three distinct normals can be drawn to the parabola y^(2)-2y=4x-9 from the point (2a,b), then find the range of the value of a.

the distance of a focal chord of the parabola y^(2)=16x from its vertex is 4 and the length of focal chord is k ,then the value of 4/k is