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

Three normals with slopes m_1, m_2 and m_3 are drawn from a point P not on the axis of the axis of the parabola y^2 = 4x . If m_1 m_2 = alpha , results in the locus of P being a part of parabola, Find the value of alpha

If the line y=m x+1 is tangent to the parabola y^2=4x , then find the value of m .

Normals are drawn from the interior point P to the parabola y^(2)=4x such that product of two slope is alpha , if locus of P is parabola itself then alpha is _________

If the line y=m x+1 is tangent to the parabola y^2=4x , then find the value of mdot

Two tangents are drawn from a point (-4, 3) to the parabola y^(2)=16x . If alpha is the angle between them, then the value of cos alpha is

Let tangent PQ and PR are drawn from the point P(-2, 4) to the parabola y^(2)=4x . If S is the focus of the parabola y^(2)=4x , then the value (in units) of RS+SQ is equal to

If tangents be drawn from points on the line x=c to the parabola y^2=4x , show that the locus of point of intersection of the corresponding normals is the parabola.

If two tangents drawn from the point P (h,k) to the parabola y^2=8x are such that the slope of one of the tangent is 3 times the slope of the other , then the locus of point P is

The number of normals drawn to the parabola y^(2)=4x from the point (1,0) is