Three normals with slopes `m_1, m_2 and m_3` are down 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`

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_(1)m_(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

The set of points on the axis of the parabola (y-2)^2=4(x-1/2) from which three distinct normals can be drawn to the parabola are

A normal of slope 4 at a point P on the parabola y^(2)=28x , meets the axis of the parabola at Q. Find the length PQ.

The set of points on the axis of the parabola y^2-4x-2y+5=0 from which all the three normals to the parabola are real , is

Equation of normal to the parabola y^(2)=4ax having slope m is

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 _________

The locus of the mid-point of the chords of the parabola x^(2)=4py having slope m, is a

From the point P(h, k) three normals are drawn to the parabola x^(2) = 8y and m_(1), m_(2) and m_(3) are the slopes of three normals Find the algebraic sum of the slopes of these three normals.