Prove that through any point, three normals can be drawn to a parabola and the algebraic sum of the ordinates of the three points is zero.

From a point (sintheta,costheta) , if three normals can be drawn to the parabola y^(2)=4ax then the value of a is

A circle and a parabola y^(2)=4ax intersect at four points.Show that the algebraic sum of the ordinates of the four points is zero.Also show that the line joining one pair of these four points is equally inclined to the axis.

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.

From a point (h,k) three normals are drawn to the parabola y^2=4ax . Tangents are drawn to the parabola at the of the normals to form a triangle. The centroid G of triangle is

Three normals are drawn to the parabola y^(2) = 4x from the point (c,0). These normals are real and distinct when

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.