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KCET2011MathematicsApplication of Derivatives

The angle between y²=4 x and x²+y²=12 at a point of their intersection is

Options

  1. A⁻¹ 2
  2. B⁻¹ 2
  3. C⁻¹ 2 2
  4. D⁻¹ ( 1 2 )

Correct answer

C. ⁻¹ 2 2

Step-by-step solution

Given equation of curve is and gathered y²=4 x x²+y²=12 gathered Let the slope of curve (i) is m₁ and curve (ii) is (m₂ ) . Then, from Eqs. (i) and (ii), 2 y d y d x =4 m₁= 2 y and m₂= -x y Let the angle between curve at intersection point is ' . aligned &= | m₁-m₂ 1+m₁ m₂ |= | 2 / y-(-x / y) 1+(2 / y)(-x / y) | &= | 2 y + x y 1- 2 x y² |= | (2+x) y y²-2 x | (iii) aligned On solving Eqs. (i) and (ii), we get aligned x²+4 x=12 & x²+4 x-12=0 & x²+6 x-2 x-12=0 &(x+6)(x-2)=0 &x=-6,2 (here x -6) & y= 2 2 aligned So, the

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