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Vector Algebra

Question
CBSEENMA12032915

Represent the following family of curves by forming the corresponding differential equations (a. b: parameters).
straight x over straight a plus straight y over straight b equals 1


Solution
The equation of given curve is
straight x over straight a plus straight y over straight b equals 1
Differential w.r.t x, we get,
1 over straight a plus 1 over straight b dy over dx equals 0
Again differentiating w.r.t x, we get.
0 plus 1 over straight b fraction numerator straight d squared straight y over denominator dx squared end fraction equals 0                       rightwards double arrow space space space space fraction numerator straight d squared straight y over denominator dx squared end fraction space equals space 0
which is required differential equation.