Maths-
General
Easy

Question

The foci of the ellipse 25 (x + 1)2 + 9 (y + 2)2 = 225 are

  1. (-1, 2), (6, 1)    
  2. (-1, -2), (1, 6)    
  3. (1, -2), (1, - 6)    
  4. (-1, 2), (-1, -6).    

Hint:

Convert the given equation into standard form and find c

The correct answer is: (-1, 2), (-1, -6).


     Given : 
    25 space left parenthesis x space plus space 1 right parenthesis squared space plus space 9 space left parenthesis y space plus space 2 right parenthesis squared space equals space 225 D i v i d i n g space b y space 225 space o n space b o t h space s i d e s
rightwards double arrow space left parenthesis x space plus space 1 right parenthesis squared over 9 space plus space fraction numerator space left parenthesis y space plus space 2 right parenthesis squared over denominator 25 end fraction space equals space 1
rightwards double arrow L e t space X space equals space left parenthesis x space plus 1 right parenthesis space a n d space Y space equals space left parenthesis y space plus 2 right parenthesis
rightwards double arrow X squared over 9 space plus space fraction numerator space Y squared over denominator 25 end fraction space equals space 1
H e r e space a squared space less than space b squared space comma w h i c h space m e a n s space t h a t space t h e space m a j o r space a x i s space o f space t h e space e l l i p s e space l i e s space a l o n g space t h e space y minus a x i s.
rightwards double arrow x squared over b squared space plus space y squared over a squared space equals space 1
w h e r e space b space equals space 3 space a n d space a space equals space 5
T h e r e f o r e comma space
rightwards double arrow c space equals space square root of a squared minus b squared end root
rightwards double arrow c equals space plus-or-minus 4
F o c i space a r e space left parenthesis X space equals space 0 space comma space Y space equals space plus-or-minus c right parenthesis space
rightwards double arrow left parenthesis x space plus space 1 space equals space 0 comma space y plus 2 space equals space plus-or-minus 4 right parenthesis
T h u s comma space t h e space p o i n t s space a r e space left parenthesis negative 1 comma 2 right parenthesis space a n d space left parenthesis negative 1 comma negative 6 right parenthesis
     Thus, the foci of the ellipse 25 (x + 1)2 + 9 (y + 2)2 = 225 are   (-1, 2), (-1, -6).

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    Error converting from MathML to accessible text. Thus, we get the sum of total numbers greater than 10000 formed by using digits 1, 3, 5, 7, 9 without repetition is 6666600.
    Error converting from MathML to accessible text.



     

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