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1)

A vertical line passing through the point (h,o) intersects the ellipse   x24+y23=1  at the points P and Q .Let the tangents to the ellipse at P and Q meet at the point R.If   (h)  = area of the   PQR , 1=max(h) .   2=min1/2h1(h)1/2h1  , then 

85182 is equal to 


A) 9

B) 4

C) 8

D) 5

Answer:

Option A

Explanation:

Concept involved

 As to maximise or minimise area of triangle we sholud find area is terms of parametric coordinate and we second derivative test.

 Here , tangent at   P(2cosθ,3sinθ) is  

952021186_m10.JPG

x2cosθ+y3sinθ=1

     R(secθ,0)

     =areaofPQR

  =12(23sinθ)(2secθ2cosθ)

    =23.sin3θcosθ   .........(i)

  Since,   12h1,

       122cosθ1,

        14cosθ12

   ddθ=23{cosθ.3sin3θcosθsin3θ(sinθ)}cos2θ

    =   23sin2θcos2θ[3cos2θ+sin2θ]

    =   23sin2θcos2θ[2cos2θ+1]

    =  23tan2θ(2cos2θ+1)>0

   when, 14cosθ12

   1=max   occurs at cos θ = 14

(23sin3θcosθ)

when   cosθ=14=4558

2=min   occurs at cos θ = 12

 =  (23sin3θcosθ)

 when    cosθ=12=92

   85182=4536=9