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KCET2013MathematicsApplication of Derivatives

If ⁻¹ a is the acute angle between the curves x²+y²=4 x and x²+y²=8 at (2,2) , then a is equal to

Options

  1. A1
  2. B0
  3. C1 2
  4. D3 2

Correct answer

C. 1 2

Step-by-step solution

Given curves are, x²+y²=4 x...(i) On differentiating w.r.t. x , we get 2 x+2 y d y d x =4 d y d x = 2-x y At (2,2), ( d y d x )_ (2,2) = 2-0 2 =0=m₁ and x²+y²=8 On differentiating w.r.t. x , we get aligned 2 x+2 y d y d x &=0 d y d x &= -x y aligned At (2,2) ( d y d x )_ (2,2) = -2 2 =-1=m₂ Let be an acute angle between the given curves, then, we get array cc & = | m₁-m₂ 1+m₁ m₂ |= | 0+1 1+0 |=1 & = 45^ & =45^ array ⁻¹(a)=45^ (given . = ⁻¹ a ) a= 45^ a= 1 2

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