Choose the correct statement about two circles whose equations are given below.

Question

Choose the correct statement about two circles whose equations are given below.
$$x^2+y^2-10x-10y+41=0,\qquad x^2+y^2-22x-10y+137=0$$

Accepted Answer

Circle 1: centre $(5,5)$, $r_1^2=25+25-41=9\Rightarrow r_1=3$. Circle 2: centre $(11,5)$, $r_2^2=121+25-137=9\Rightarrow r_2=3$.

Distance between centres $=6=r_1+r_2$ --- the circles touch externally, so they have exactly one meeting point.

Solutions · 1