Question

Find the differential equation by eliminating arbitrary constants from the relation x² + y² = 2ax

Answer 1

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.