CircleEasy
Question
The centres of a set of circles, each of radius 3, lie on the circle x2 + y2 = 25. The locus of any point in the set is
Options
A.4 ≤ x2 + y2 ≤ 64
B.x2 + y2 ≤ 25
C.x2 + y2 ≥ 25
D.3 ≤ x2 + y2 ≤ 9
Solution
Let (h, k) be the centre of any such circle. Equation of such circle is (x - h)2 + (y - k)2 = 32. Since (h, k) lies on x2 + y2 = 25 ∴ h2 + k2 = 25.
x2 + y2 - (2xh + 2yk) + 25 = 9 ; Locus of (h, k) is x2 + y2 = 16, which clearly satisfies (a).
x2 + y2 - (2xh + 2yk) + 25 = 9 ; Locus of (h, k) is x2 + y2 = 16, which clearly satisfies (a).
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