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T h e space e c c e n t r i c i t y space o f space t h e space h y p e r b o l a space space x squared over a squared minus y squared over b squared equals 1 space space space b e space r e c i p r o c a l space t o space t h a t space o f space t h e space e l l i p s e space x squared plus 4 y squared space equals 4. space I f space t h e space h y p e r b o l a space p a s s e s space t h r o u g h space t h e space f o c u s space o f space t h e space e l l i p s e comma space t h e n space f i n d space t h e space v a l u e s space a space a n d space b space a n d space h e n c e 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 h y p e r b o l a space.

Asked by surajsubedi14 8th March 2015, 2:09 PM
Answered by Expert
Answer:
x squared over a squared minus y squared over b squared equals 1 E c c e n t r i c i t y space o f space t h e space h y p e r b o l a comma space e squared equals 1 plus b squared over a squared e equals square root of 1 plus b squared over a squared end root x squared plus 4 y squared equals 4 x squared over 4 plus y squared over 1 equals 1 a apostrophe equals 2 comma b apostrophe equals 1 E c c e n t r i c i t y space o f space t h e space e l l i p s e comma space e apostrophe squared equals 1 minus 1 fourth e apostrophe squared equals 3 over 4 e apostrophe equals fraction numerator square root of 3 over denominator 2 end fraction e equals fraction numerator 1 over denominator e apostrophe end fraction square root of 1 plus b squared over a squared end root equals fraction numerator 1 over denominator fraction numerator square root of 3 over denominator 2 end fraction end fraction 1 plus b squared over a squared equals 4 over 3 fraction numerator a squared plus b squared over denominator a squared end fraction equals 4 over 3 3 a squared plus 3 b squared equals 4 a squared a squared equals 3 b squared E c c e n t r i c i t y space o f space t h e space h y p e r b o l a comma space e equals square root of 1 plus b squared over a squared end root equals square root of 1 plus fraction numerator b squared over denominator 3 b squared end fraction end root equals square root of 1 plus 1 third end root equals fraction numerator 2 over denominator square root of 3 end fraction F o c u s space o f space t h e space e l l i p s e comma left parenthesis a apostrophe e apostrophe comma 0 right parenthesis open parentheses 2 cross times fraction numerator square root of 3 over denominator 2 end fraction comma 0 close parentheses equals open parentheses square root of 3 comma 0 close parentheses T h e space h y p e r b o l a space p a s s e s space t h r o u g h space f o c u s space i f space t h e space e l l i p s e comma space x squared over a squared minus y squared over b squared equals 1 I t space p a s s e s space t h r o u g h space open parentheses square root of 3 comma 0 close parentheses 3 over a squared equals 1 a equals square root of 3 b equals 1 E c c e n t r i c i t y space o f space t h e space h y p e r b o l a equals fraction numerator 2 over denominator square root of 3 end fraction
Answered by Expert 8th March 2015, 10:12 PM
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