Three normals drawn from a point (h k) to parabola `y^2 = 4ax`

Three normals drawn from a point (hk) to parabola y^(2)=4ax

If three normals are drawn from point (h,0) on parabola y^(2)=4ax, then h>2a and one of the normal is axis of the parabola and other two are equally inclined to the axis of the parabola.Prove it?

If 27ak^(2)<4(h-2a)^(3) satisfied then three real and distinct normal are drawn from point (h,k) on parabola y^(2)=4ax

If normal are drawn from a point P(h,k) to the parabola y^(2)=4ax, then the sum of the intercepts which the normals cut-off from the axis of the parabola is (h+c) (b) 3(h+a)2(h+a)( d) none of these

If two normals drawn from any point to the parabola y^(2) = 4ax make angle alpha and beta with the axis such that tan alpha . tan beta = 2, then find the locus of this point,

Show that the locus of points such that two of the three normals drawn from them to the parabola y^2 = 4ax coincide is 27ay^2 = 4(x-2a)^3 .

If two of the three feet of normals drawn from a point to the parabola y^(2)=4x are (1,2) and (1,-2), then find the third foot.

If three normals are drawn from the point (c, 0) to the parabola y^(2)=4x and two of which are perpendicular, then the value of c is equal to

Three normals are drawn from the point (7, 14) to the parabola x^(2)-8x-16y=0. Find the coordinates of the feet of the normals.