Revisiting coordinate 2

Geometry Level 5

Normals are drawn to a parabola at points ( 0 , 0 ) (0,0) and ( 3 , − 1 ) (3,-1) . The normals intersect each other at ( 1 , 1 ) (1,1) .

If the coordinates of focus of the parabola is ( a , b ) (a,b) , find a + b a+b .


The answer is 1.6.

Prakhar Bindal by Prakhar Bindal , 22, India

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1 solution

We can easily observe that,normals are perpendicular to each other.Therefore tangents at these points will intersect at right angles on the directrix.Foot of perpendicular from this point on directrix to the chord joining the points on parabola will be the focus. Good question on coordinate geometry!!!

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