Question

A circle $S$ of radius $2$ units lies in the first quadrant and touches both the coordinate axes. The equation of the circle with centre at $(6,5)$ and touching the circle $S$ externally is

• A. $x^2+y^2-12x-10y+12=0$
• B. $x^2+y^2-12x-10y-20=0$
• C. $x^2+y^2-12x-10y+25=0$
• D. $x^2+y^2-12x-10y+52=0$

Answer 1

Answer: (D)

From figure

Centre of given circle $\left(C_1\right)=(2,2)$ radius $=2$ units
Centre of required circle $\left(C_2\right)=(6,5)$
$C_1{C}_2=r+2$
$5=r+2$
$\therefore r=3$
$\therefore$ Required equation of circle having centre at $(6,5)$ and $r=3$ is
$(x-6{)}^2+(y-5{)}^2=3^2$
$x^2+y^2-12x-10y+52=0$