Question
The eccentricity of the curve represented by the equation x2 + 2y2 – 2x + 3y + 2 = 0 is
- 0
Hint:
To find eccentricity first convert the equation into standard form i.e.
![x squared over a squared space plus space y squared over b squared space equals space 1](data:image/png;base64,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)
The correct answer is: ![fraction numerator 1 over denominator square root of 2 end fraction](data:image/png;base64,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)
To find eccentricity first convert the equation into standard form i.e.
![x squared over a squared space plus space y squared over b squared space equals space 1](data:image/png;base64,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)
Given :
![rightwards double arrow x squared space plus space 2 y squared space – space 2 x space plus space 3 y space plus space 2 space equals space 0
rightwards double arrow x squared space – space 2 x space plus 1 space minus 1 plus space space 2 left parenthesis y squared plus space 3 over 2 y right parenthesis space plus space 2 space equals space 0
rightwards double arrow left parenthesis x squared space – space 2 x space plus 1 right parenthesis space plus space space 2 left parenthesis y squared plus space 3 over 2 y right parenthesis space plus space 2 space equals space 1
rightwards double arrow left parenthesis x minus 1 right parenthesis squared space plus space 2 left parenthesis y squared space plus space 2 cross times 3 over 2 y space plus 9 over 4 space minus 9 over 4 right parenthesis space plus space 2 space equals space 1
rightwards double arrow left parenthesis x minus 1 right parenthesis squared space plus space 2 left parenthesis y space plus space 3 over 4 right parenthesis squared space minus 9 over 8 space equals space 1
rightwards double arrow left parenthesis x minus 1 right parenthesis squared space plus space 2 left parenthesis y space plus space 3 over 4 right parenthesis squared space space equals space 1 over 8
D i v i d i n g space b y space 1 over 8
rightwards double arrow fraction numerator left parenthesis x minus 1 right parenthesis squared over denominator begin display style 1 over 8 end style end fraction space plus fraction numerator space left parenthesis y space plus space 3 over 4 right parenthesis over denominator begin display style 1 over 16 end style end fraction squared space space equals space 1](data:image/png;base64,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)
Comparing with standard form
![a squared space equals space 1 over 8 space a n d space b squared space equals space 1 over 16](data:image/png;base64,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)
![e space equals space square root of 1 space minus space b squared over a squared end root
e space equals space square root of 1 minus space fraction numerator begin display style bevelled 1 over 16 end style over denominator begin display style bevelled 1 over 8 end style end fraction end root space equals square root of 1 minus space 8 over 16 end root space equals space square root of 8 over 16 end root space equals space fraction numerator 1 over denominator square root of 2 end fraction
T h u s comma space T h e space e c c e n t r i c i t y space o f space t h e space c u r v e space r e p r e s e n t e d space b y space t h e space e q u a t i o n space x squared space plus space 2 y squared space – space 2 x space plus space 3 y space plus space 2 space equals space 0 space i s space space fraction numerator 1 over denominator square root of 2 end 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Related Questions to study
The foci of the ellipse 25 (x + 1)2 + 9 (y + 2)2 = 225 are
The foci of the ellipse 25 (x + 1)2 + 9 (y + 2)2 = 225 are
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.