Form the differential equation corresponding to (x – a) 2 + (y – b) 2 = r 2 by eliminating a and b.

Question

Philoid · Accepted Answer

(x – a)² + (y – b)² = r² …… (i)

On differentiating with respect to x, we get,

Again, differentiating with respect to x we get,

Put the value of (y – b) obtained in (ii) we get,

Put the value of (x – a) and (y – b) in (i) we get,

Put we get,

⇒ (y’³ + y’)² + (y’² + 1)² = r²y’’²

So, the required differential equation is (y’³ + y’)² + (y’² + 1)² = r²y’’².