Q9 of 184 Page 10

Prove that the distance between the points (a + rcosθ, b + rsinθ) and (a, b) is independent of θ.

Given points are A(a + rcosθ, b + rsinθ) and B(a, b).



We know that the distance between the points (x1, y1) and (x2, y2) is







⇒ AB = r


We can see that AB is independent of θ.


∴ Thus proved.


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