CircleHard
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).
Create a free account to view solution
View Solution FreeMore Circle Questions
If the pair of lines ax2 + 2(a + b)xy + by2 = 0 lie along diameters of a circle and divide the circle into four sectors ...Equation (2 + λ)x2 - 2λxy + (λ - λ)y2 - 4x - 2 = 0 represents a hyperbola if -...One possible equation of the chord of x2 + y2 = 100 that passes through (1, 7) and subtends an angleat origin is -...The equation of director circle to the circle x2 + y2 = 8 is-...The tangent to the hyperbola, x2 - 3y2 = 3 at the point (√3, 0) when associated with two asymptotes constitutes -...