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AP EAMCET2011MathematicsHyperbola

The angle between the asymptotes of the hyperbola x^2-3 y^2=3 is

Options

  1. A6
  2. B4
  3. C3
  4. D2

Correct answer

C. 3

Step-by-step solution

Given equation of hyperbola is aligned x^2-3 y^2 & =3 x^2 3 - y^2 1 & =1 aligned Here, a^2=3 and b^2=1, a>b . Now, the equation of asymptote of this hyperbola is, aligned y & = b a x y & = 1 3 x aligned Let slope of asymptote (i) is, m₁= 1 3 and slope of asymptote (ii) is, m₂= -1 3 Let be the angle between both asymptote, then = | m₁-m₂ 1+m₁ m₂ |= | 1 / 3 +1 / 3 1-1 / 3 | array cc & = | 2 / 3 2 / 3 |= 3 & = 60^ & = / 3 array

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