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If is the acute angle between the curves x^2+y^2=4 and y^2=3 x then =

Options

  1. A5 3
  2. B3 4
  3. C4 3
  4. D3 5

Correct answer

A. 5 3

Step-by-step solution

Given curves are x^2+y^2=4 and y^2=3 x Put the value of y^2 . aligned & x^2+3 x-4=0 & x^2+4 x-x-4=0 & x(x+4)-1(x+4)=0 & (x-1)(x+4)=0 & x-1=0, x+4=0 & x=1, x=-4 aligned Put in y^2=3 x , then, y^2=3, y= 3 . (x, y) (1, 3 ) &(1, 3 ) Now, Differentiate both curves w.r.t x aligned & x^2+y^2=4 & 2 x+2 y d y d x =0 & y d y d x =-x & d y d x =- x y & y= 3 x & d y d x = 3 2 x aligned Put the point (1, 3 ) in their differentiation. aligned & m₁= d y d x = -1 3 , m₂= 3 2 & = | m₁-m₂ 1+m₁ m₂ |= | - 1 3 - 3 2 1- 1 3 3 2 |= | -2-

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