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CBSE Class 11-science Answered

F i n d space t h e space e q u a t i o n space o f space t h e space h y p e r b o l a space w i t h space X minus a x i s space a s space t h e space t r a n s v e r e space a x i s space c e n t e r e d space a t space o r i g i n comma space p o i n t space left parenthesis 3 comma 1 right parenthesis
l i e s space o n space t h e space h y p e r b o l a space a n d space left parenthesis 4 comma 2 right parenthesis space l i e s space o n space t h e space a s y m p t o t e space o f space t h i s space h y p e r b o l a

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Asked by Topperlearning User | 17 Nov, 2016, 02:14: AM
Expert Answer

T h e space h y p e r b o l a space w i t h space X minus a x i s space a s space t h e space t r a n s v e r e space a x i s space c e n t e r e d space a t space o r i g i n
i s space o f space t h e space f o r m space x squared over a squared minus y squared over b squared equals 1
T h e space a s y m p t o t e s space o f space t h i s space h y p e r b o l a space w i l l space b e space o f space t h e space f o r m space y equals plus-or-minus b over a x
G i v e n space left parenthesis 3 comma 1 right parenthesis space l i e s space o n space t h e space h y p e r b o l a space s o
9 over a squared minus 1 over b squared equals 1
rightwards double arrow 9 b squared minus a squared equals a squared b squared
G i v e n space left parenthesis 4 comma 2 right parenthesis space l i e s space o n space t h e space a s y m p t o t e space s o space w e space h a v e space t o space t a k e space t h e space a s y m p t o t e
w i t h space p o s i t i v e space s l o p e space a s space t h e space p o i n t space l i e s space i n space t h e space f i r s t space q u a d r a n t space s o
2 equals b over a 4
rightwards double arrow a equals 2 b
9 b squared minus a squared equals a squared b squared
rightwards double arrow 9 b squared minus 4 b squared equals 4 b to the power of 4
rightwards double arrow b squared equals 5 over 4
a squared equals 5
T h e space r e q u i r e d space e q u a t i o n space i s space x squared over 5 minus fraction numerator 5 y squared over denominator 4 end fraction equals 1

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