The centres of a set of circles, each of radius 3, lie on the circle `x^2+y^2+25`. The locus of any point in the set is: (a) `4lex^(2)+y^(2)le64` (b) `x^(2)+y^(2)le25` (c) `x^(2)+y^(2)ge25` (d) `3 lex^(2)+y^(2)le9`

Options

A. `4 le x^(2)+y^(2) le 64`
B. `x^(2)+y^(2) le 25`
C. `x^(2)+y^(2)ge 25`
D. `3 le x^(2) + y^(2) le 9`

Answer

A

Explanation

Let P (h, k) be any point of a circle of radius 3 units and having its centre on `x^(2)+y^(2)=25`. Then,
`5-3 le OP le 5 + 3`
`rArr 2 le OP 8 rArr 4 le OP^(2) le 64 rArr 4 le h^(2) + k^(2) le 64`
Hence, the locus of P (h, k) is `4 le x^(2)+y^(2) le 64`.