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Vector Algebra

Question
CBSEENMA12032925

Represent the following family of curves by forming the corresponding differential equations (a. b: parameters).
straight x squared plus straight y squared space equals space 2 ax







Solution

The given equation is
                       straight x squared plus straight y squared space equals space 2 ax                    ...(1)
Differentiating both sides w.r.t. x, we get,
                     2 straight x plus 2 straight y dy over dx space equals space 2 straight a               ...(2)
Putting value of 2a from (2) in (1), we get,
                        straight x squared plus straight y squared space equals space open parentheses 2 straight x plus 2 straight y dy over dx close parentheses straight x
or            straight x squared plus straight y squared space equals space 2 straight x squared plus 2 xy dy over dx space space space space or space space space 2 xy dy over dx plus straight x squared minus straight y squared space equals space 0
which is the required differential equation.