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Question
Find the differential equation by eliminating arbitrary constants from the relation x2 + y2 = 2ax
Solution
Given relation is
x2 + y2 = 2ax .....(i)
Differentiating w.r.t. x, we get
`2x + 2y ("d"y)/("d"x)` = 2a ......(ii)
Substituting (ii) in (i), we get
x2 + y2 = `(2x+ 2y ("d"y)/("d"x))x`
∴ x2 + y2 = `2x^2+ 2xy ("d"y)/("d"x)`
∴ `2xy ("d"y)/("d"x)` = y2 – x2, which is the required differential equation.
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