Q)

Asked by araima2001 | 30th Mar, 2017, 05:28: AM

Expert Answer:

begin mathsize 16px style Let space straight R left parenthesis straight x comma 0 right parenthesis space be space the space point space as space it space touches space the space straight x minus axis space straight y minus coordinate space will space be space zero.
PR plus RQ equals square root of open parentheses straight x plus 3 close parentheses squared plus open parentheses 0 minus 4 close parentheses squared end root plus square root of straight x squared plus 1 end root
space space space space space space space space space space space space space space space space space equals square root of open parentheses straight x plus 3 close parentheses squared plus 16 end root plus square root of straight x squared plus 1 end root
space space space space space space space space space space space space space space space space space space equals square root of straight x squared plus 6 straight x plus 25 end root plus square root of straight x squared plus 1 end root
Differentiating space with space respect space to space straight x comma
fraction numerator 1 over denominator 2 square root of straight x squared plus 6 straight x plus 25 end root end fraction cross times open parentheses 2 straight x plus 6 close parentheses plus fraction numerator 1 over denominator 2 square root of straight x squared plus 1 end root end fraction cross times 2 straight x
fraction numerator straight x plus 3 over denominator square root of straight x squared plus 6 straight x plus 25 end root end fraction plus fraction numerator straight x over denominator square root of straight x squared plus 1 end root end fraction equals 0
Now space find space the space value space of space straight x space
left parenthesis straight x plus 3 right parenthesis square root of straight x squared plus 1 end root plus straight x square root of straight x squared plus 6 straight x plus 25 end root equals 0
left parenthesis straight x plus 3 right parenthesis square root of straight x squared plus 1 end root equals negative straight x square root of straight x squared plus 6 straight x plus 25 end root
Squaring space on space both space sides space and space simplifying space you space will space get space straight x equals space fraction numerator negative 3 over denominator 5 end fraction
So space the space answer space is space left parenthesis fraction numerator negative 3 over denominator 5 end fraction comma 0 right parenthesis
Taking space second space derivative space you space can space show space that space at space straight x equals fraction numerator negative 3 over denominator 5 end fraction it space is space greater space than space zero.
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Answered by Sneha shidid | 30th Mar, 2017, 12:52: PM