Question

The locus of the centres of all circles of given radius a, in the same plane, passing through a fixed point, is:

• A. A point
• B. A straight line
• C. Two straight lines
• D. A circle
• E. Two circles

Answer 1

The correct option is D A circle

Let the centre of circle (h,b)

and fixed point (s,t)

Distance between centre and fixed point = radius

$\sqrt{(h-s{)}^{{}_2}+(t-b{)}^{{}_2}}=a$

$(h-s{)}^2+(b-t{)}^2=a^2$

Here locus of centre is circle having centre as fixed point.

$(x-s{)}^2+(y-t{)}^2=a^2$