General
General
Easy

Question

The equation of the tangents drawn at the ends of the major axis of the ellipse 9x2 + 5y2 – 30y = 0 is

  1. y = ± 3    
  2. x = ± square root of 5    
  3. y = 0, y = 6    
  4. none of these    

hintHint:

Convert the given equation in standard form i.e.
x squared over a squared space plus space y squared over b squared space equals space 1

The correct answer is: y = 0, y = 6


     Given : 9 x squared space plus space 5 y squared space – space 30 y space equals space 0 space
    Adding and subtracting the above by 45
    9 x squared space plus space 5 y squared space – space 30 y space plus space 45 space minus 45 space equals space 0 space
9 x squared space plus space 5 left parenthesis y squared space – space 6 y space plus space 9 right parenthesis space equals space 45
9 x squared space 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 y space 45 space o n space b o t h space s i d e s comma space w e space g e t
x squared over 5 space plus space open parentheses y minus 3 close parentheses squared over 9 space equals space 1
    Center coordinates = (0,3)
    At x = 0
    open parentheses y minus 3 close parentheses squared space equals space 9
    On solving we get :
    rightwards double arrow space y space equals space 0 comma 6
    T h e r e f o r e comma space tan g e n t s space a t space v e r t e x space a r e space y equals 0 comma y equals 6.

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