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Prove that the tangents at the end of latus rectum of parabola intersect on directrix at right angle

Prove that the tangents at the end of latus rectum of parabola intersect on directrix at right angle

Grade:12th pass

1 Answers

prince kumar
23 Points
6 years ago
equation of tangent   Y=mx+a/m
 then, 
          let point (H,K) where both tangent intesect each other 
              now, (X,Y) replace through(H,K)
         THEN , equation of tangent is K=hm+a/m
ater solve it  then 
    equation is  hm2 -km +a=0
m1 * m2= -1 then 
a/h=-1
a=-h 
a+h=0 
(H) replace with x
x+a=0
IT IS EQATION OF DIRECTRICS.
HENCE, IT IS PROVED.

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