Let ax-y+7=0 be a chord of parabola x^2=28y
meeting it at A and B ,and tangents at A and B meet at C.the locus of circumcentre of tr.ABC is

Let us first solve for end points of the chord by finding points of intersection of chord and parabola:

It is also interesting to note
Let’s now call the slope of tangents at these two points –

So it is easy to see that

Thus, the two tangents are perpendicular and tr.ABC is a right-angled triangle.
AND

Circumcenter of a right-angled triangle is the midpoint of the hypotenuse.

This gives, for the coordinates of circumcenter,

Thus, the locus is a parabola given in parametric form above.