Question

The two circles $x^2+y^2-2x+6y+6=0$ and $x^2+y^2-5x+6y+15=0$ touch each other

• A. Externally
• B. Internally
• C. Coincide
• D. None of these

Answer 1

The correct option is B Internally

Given equation of circles are
$x^2+y^2-2x+6y+6=0$ .....(i)
and $x^2+y^2-5x+6y+15=0$ ..... (ii)
The centre and radius of the Ist circle are $C_1(1,-3)$ and $2$.
The centre and radius of the IInd circle are $C_2(\frac{5}{2},-3)$ and $\frac{1}{2}$.
$\therefore$ The distance between the centres
$C_1{C}_2=\sqrt{{(1-\frac{5}{2})}^2+(-3+3{)}^2}$
$=\sqrt{\frac{9}{4}}=\frac{3}{2}$
Since, the distance between their centres is equal to the difference of their radii.
$\therefore$ The circles touch each other internally.