If (x – a)² + (y – b)² = c², for some c > 0, prove that

is a constant independent of a and b.

Given: (x – a)² + (y – b)² = c²

To prove: is a constant independent of a and b

(x – a)² + (y – b)² = c²

Differentiating both sides with respect to x:

Again differentiating both sides with respect to x:

{∵ (x – a)² + (y – b)² = c²}

Now,

{∵ (x – a)² + (y – b)² = c²}

= -c

So, clearly , which is independent of a and b

Hence Proved