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Continuity And Differentiability

Question

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$Find space dy over dx where space space space ax squared plus 2 hxy plus by squared plus 2 gx plus 2 fy plus straight c equals 0$

Solution

Here space space ax squared plus 2 hxy plus by squared plus 2 gx plus 2 fy plus straight c equals 0 Differentiatinfg space both space sides space straight w. straight r. straight t. straight x comma space we space get comma space 2 ax plus 2 straight h open parentheses straight x dy over dx plus straight y.1 close parentheses plus 2 by dy over dx plus 2 straight g.1 plus 2 straight f plus 0 equals 0 therefore space ax plus hx dy over dx plus hy plus by dy over dx plus straight g plus straight f dy over dx equals 0 therefore space left parenthesis hx plus by plus straight f right parenthesis dy over dx equals negative left parenthesis ax plus hy plus straight g right parenthesis rightwards double arrow space dy over dx equals negative fraction numerator ax plus hy plus straight g over denominator hx plus by plus straight f end fraction

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