Normals are drawn from the point P with slopes `m_(1),m_(2)andm_(3)` to that parabola `y^(2)=4x`. If the locus of P with `m_(1)m_(2)=alpha` is a part of the parabola itself then the value of `alpha` is _________.

Normals are drawn from a point P with slopes m_1,m_2 and m_3 are drawn from the point p not from the parabola y^2=4x . For m_1m_2=alpha , if the locus of the point P is a part of the parabola itself, then the value of alpha is (a) 1 (b)-2 (c) 2 (d) -1

What is the length of the focal distance from the point P(x_(1),y_(1)) on the parabola y^(2) =4ax ?

The angle between the tangents drawn from the point (1, 4) to the parabola y^(2)=4x is -

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 position of points P(1,3) w.r.t. parabolas y^(2)=4x and x^(2)=8y .

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

If the point P(4, -2) is the one end of the focal chord PQ of the parabola y^(2)=x, then the slope of the tangent at Q, is

P(alpha,alpha) is a point on the parabola y^(2)=4ax . Show that the normal chord of the parabola at P subtends a right angle at its focus.

Normals are drawn at points A, B, and C on the parabola y^2 = 4x which intersect at P. The locus of the point P if the slope of the line joining the feet of two of them is 2, is

Find the locus of the point from which the two tangents drawn to the parabola y^2=4a x are such that the slope of one is thrice that of the other.