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`

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

The set of points on the axis of the parabola y^2 =4ax , from which three distinct normals can be drawn to theparabola y^2 = 4ax , is

Find the point on the axis of the parabola 3y^2+4y-6x+8 =0 from where three distinct normals can be drawn.

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

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.

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

The set of points on the axis of the parabola y^2-4x-2y+5=0 find the slope of normal to the curve at (0,0)

A normal drawn at a point P on the parabola y^2 = 4ax meets the curve again at Q. The least distance of Q from the axis of the parabola, is

A normal drawn at a point P on the parabola y^2 = 4ax meets the curve again at Q. The least distance of Q from the axis of the parabola, is

From a point P, two tangents are drawn to the parabola y^(2) = 4ax . If the slope of one tagents is twice the slope of other, the locus of P is