Q15 of 147 Page 191

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


Differentiating with respect to x, we get



⇒


⇒


∴


Differentiating again with respect to x



Using Quotient Rule


⇒


⇒


Substituting the value of dy/dx in the above equation


⇒


⇒


∴


∴ , which is independent of a and b


Hence, Proved


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