Question
The foci of the ellipse 25 (x + 1)2 + 9 (y + 2)2 = 225 are
- (-1, 2), (6, 1)
- (-1, -2), (1, 6)
- (1, -2), (1, - 6)
- (-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](data:image/png;base64,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)
Thus, the foci of the ellipse 25 (x + 1)2 + 9 (y + 2)2 = 225 are (-1, 2), (-1, -6).
Related Questions to study
The eccentricity of the ellipse 9x2 + 5y2 – 30y = 0 is
The eccentricity of the ellipse 9x2 + 5y2 – 30y = 0 is
The sum of all possible numbers greater than 10,000 formed by using {1,3,5,7,9} is
The sum of all possible numbers greater than 10,000 formed by using {1,3,5,7,9} is
Number of different permutations of the word 'BANANA' is
In this question, one might think that the total number of permutations for the word BANANA is 6!
This is wrong because in the word BANANA we have the letter A repeated thrice and the letter N repeated twice.
Number of different permutations of the word 'BANANA' is
In this question, one might think that the total number of permutations for the word BANANA is 6!
This is wrong because in the word BANANA we have the letter A repeated thrice and the letter N repeated twice.
The number of one - one functions that can be defined from
into
is
The number of one - one functions that can be defined from
into
is
Four dice are rolled then the number of possible out comes is
Four dice are rolled then the number of possible out comes is
The number of ways in which 5 different coloured flowers be strung in the form of a garland is :
The number of ways in which 5 different coloured flowers be strung in the form of a garland is :
Number of ways to rearrange the letters of the word CHEESE is
Number of ways to rearrange the letters of the word CHEESE is
The number of ways in which 17 billiard balls be arranged in a row if 7 of them are black, 6 are red, 4 are white is
We cannot arrange the billiards balls as follows:
There are 17 balls, so the total number of arrangements = 17!
This is incorrect because this method is applicable only when the balls are distinct, not identical. But, in our case, all the balls of the same color are identical.
The number of ways in which 17 billiard balls be arranged in a row if 7 of them are black, 6 are red, 4 are white is
We cannot arrange the billiards balls as follows:
There are 17 balls, so the total number of arrangements = 17!
This is incorrect because this method is applicable only when the balls are distinct, not identical. But, in our case, all the balls of the same color are identical.
Number of permutations that can be made using all the letters of the word MATRIX is
Number of permutations that can be made using all the letters of the word MATRIX is
The number of different signals that can be made by 5 flags from 8 flags of different colours is :
Each of the different arrangements which can be made by taking some or all of a number of things at a time is called permutation.
Thus we can say that the permutation concerns both the selection and the arrangement of the selected things in all possible ways.
The number of different signals that can be made by 5 flags from 8 flags of different colours is :
Each of the different arrangements which can be made by taking some or all of a number of things at a time is called permutation.
Thus we can say that the permutation concerns both the selection and the arrangement of the selected things in all possible ways.