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Application Of Derivatives

Question
CBSEENMA12035139
Wired Faculty App

Find the equation of the tangent and normal to the given curves at the points given:
square root of straight x plus square root of straight y space equals space 5

Solution

The equation of curve is
                   square root of straight x plus square root of straight y space equals space 5
Differentiating both sides w.r.t x,
                            fraction numerator 1 over denominator 2 square root of straight x end fraction plus fraction numerator 1 over denominator 2 square root of straight y end fraction dy over dx space equals space 0 comma space space space space space space or space space space space fraction numerator 1 over denominator 2 square root of straight x end fraction dy over dx space equals negative fraction numerator 1 over denominator 2 square root of straight x end fraction
therefore space space space space dy over dx space equals space minus fraction numerator square root of straight y over denominator square root of straight x end fraction At space left parenthesis 9 comma space 4 right parenthesis comma space space space dy over dx space equals negative fraction numerator square root of 4 over denominator square root of 9 end fraction space equals space minus 2 over 3 comma space space space which space is space slope space of space tangent. therefore space space space space space space the space equation space of space tangent space at space left parenthesis 9 comma space 4 right parenthesis space is space space space space space space space space space space space space space space space space space space space space space straight y minus 4 space equals space minus 2 over 3 left parenthesis straight x minus 9 right parenthesis comma space space space space or space space 3 straight y minus 12 space equals space minus 2 straight x plus 18 space space space or space space space space 2 straight x plus 3 straight y minus 30 space equals space 0 Slope space of space normal space space equals space 3 over 2 therefore space space space space the space equation space of space normal space at space left parenthesis 9 comma space 4 right parenthesis space is space space space space space space space space space space space space space space space space straight y minus 4 space equals space 3 over 2 left parenthesis straight x minus 9 right parenthesis comma space space space space or space space 2 straight y minus 8 space equals space 3 straight x minus 27 space space space or space space space 3 straight x minus 2 straight y minus 19 space equals space 0

Some More Questions From Application of Derivatives Chapter

The radius of a circle is increasing uniformly at the rate of 4 cm per second Find the rate at which the area of the circle is increasing when the radius is 8 cm.

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