Maths-
General
Easy

Question

The eccentricity of the hyperbola with asymptotes 3x + 4y = 2 and 4x – 3y = 2 is

  1. 3    
  2. 2    
  3. square root of 2  square root of 2  
  4. 4    

hintHint:

The eccentricity of a hyperbola is always greater than 1. i.e. e > 1. The eccentricity of a hyperbola can be taken as the ratio of the distance of the point on the hyperbole, from the focus, and its distance from the directrix.
Eccentricity = Distance from Focus/Distance from Directrix

The correct answer is: square root of 2
 square root of 2


    We have been given two asymptotes i.e. 3x + 4y = 2 and 4x – 3y = 2
    First find out their slopes
    m 1 space equals negative space 3 over 4 space a n d space m 2 space equals space 4 over 3
    From above we can see that m1 and m2 are negative inverse of each other that means both are perpendicular to each other.
    It is a rectangular hyperbola and it has fixed eccentricity.
    Thus eccentricity = square root of 2

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