The centers 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) `4lt=x^2+y^2lt=64` (b) `x^2+y^2lt=25` (c)`x^2+y^2geq25` (d) `3lt=x^2+y^2lt=9`

Options

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`

Answer

1

Explanation

Let (h,k) be any point in the set.Then the equation of circle is `(x-h)^(2)+(y-k)^(2)=9`
But `(h,k)` lies on `x^(2)+y^(2)=25`, Therefore
`h^(2)+k^(2)=25`
`:. 2 le` Distance betwene the centres of two circles `le 8`
or `4 le h^(2)+k^(2) le64`
Therefore, the locus of (h,k) is `4lex^(2)+y^(2)le 64`.