Maths-
General
Easy

Question

The eccentricity of the ellipse 9x2 + 5y2 – 30y = 0 is

  1. fraction numerator 1 over denominator 3 end fraction    
  2. fraction numerator 2 over denominator 3 end fraction    
  3. fraction numerator 3 over denominator 4 end fraction    
  4. none of these    

Hint:

Standard form of ellipse = x squared over a squared space plus space y squared over b squared space equals space 1

The correct answer is: fraction numerator 2 over denominator 3 end fraction


     Given :
    9 x squared plus space 5 y squared space – space 30 y space equals space 0 space
C o n v e r t space i n t o space s tan d a r d space f o r m
9 x squared plus space 5 left parenthesis y squared space – space 6 y right parenthesis space equals space 0 space
9 x squared plus space 5 left parenthesis y squared space – space 6 y space plus space 9 space minus 9 right parenthesis space equals space 0 space
9 x squared plus space 5 left parenthesis y space – space 3 right parenthesis squared space equals space 45 D i v i d i n g space b o t h space s i d e s space b y space 45
x squared over 5 space space plus open parentheses y minus 3 close parentheses squared over 9 space equals space 1
a squared space equals space 5 space a n d space b squared space equals space 9
E c c e n t r i c i t y left parenthesis e right parenthesis space equals space square root of 1 minus a squared over b squared end root space equals space square root of 1 minus 5 over 9 end root space equals space square root of 4 over 9 end root space equals space 2 over 3
    Thus, the eccentricity of the ellipse 9 x squared space plus space 5 y squared space – space 30 y space equals space 0 space is 2 over 3

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