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Question

If x=secθcosθ,y=sec10θcos10θ  and (x2+4)=k(y2+4), then k is equal to
  1. 1100
  2. 1
  3. 10
  4. 100


Solution

The correct option is D 100
x2+4=(secθcosθ)2+4=(secθ+cosθ)2....(i)
Similarly, y2+4=(sec10θ+cos10θ)2....(ii)
Now,  dxdθ=secθ tanθ+sinθ=tanθ(secθ+cosθ)
and    dydθ=10sec9θ secθ tanθ10cos9θ(sinθ)
=10tanθ(sec10θcos10θ)dydx=dydθdxdθ=10 tandθ(sec10+cos10dθ)tanθ(secθ+cosθ)(dydx)2=100(sec10+cos10θ)(secθ+cosθ)2=100(y2+4)(x2+4)
                                                                   [from Eq. (i), (ii)]
or (x2+4)(dydx)2=100(y2+4)
k=100

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