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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 noteLet’s now call the slope of tangents at these two points –So it is easy to see thatThus, the two tangents are perpendicular and tr.ABC is a right-angled triangle.ANDCircumcenter 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.
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.
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