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PRADEEP KUMAR Grade:
        If a normal is drawn at a variable point P of the ellipse (X^2/a^2)+(y^2/b^2)=1,find the maximum distance of the normal from the centre of the ellipse.

6 years ago

Answers : (1)

vikas askiitian expert
510 Points
										

general point on ellipse is (x,y)= (acos@,bsin@)


  x=acos@                              &                    y =bsin@


   dx/d@=-asin@                     &                    dy/d@=bcos@


     dy/dx=-bcot@/a


slope of tangent=dy/dx=-(bcot@)/a


slope of normal=-1/dy/dx =atan@/b


now equation of normal at (acos@,bsin@) is


yb-axtan@+a2sin@-b2sin@ =0


distance of this line from center of ellipse(0,0) is


       d=  (a2-b2)sin@/(1+tan2@)1/2


         =(a2-b2)sin@/sec@=(a2-b2)sin2@ /2


maximum value of sin2@ is 1


so maximum distance is dmax= (a2-b2)/2

6 years ago
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