Question

The circles $x^2+y^2+6x+6y=0$ and $x^2+y^2-12x-12y=0$

• A. cut orthogonally
• B. touch each other internally
• C. intersect in two points
• D. touch each other externally

Answer 1

Answer: (D)

Given equation of circles are

$x^2+y^2+6x+6y=\mathrm{0...}(i)$

and $x^2+y^2-12x-12y=\mathrm{0...}(ii)$

Here, $g_1=3,f_1=3,g_2=-6$ and $f_2=-6$

$\therefore$ Centres of circles are $C_1(-3,-3)$ and $C_2(6,6)$

respectively and radii are $r_1=3\sqrt{2}$ and $r_2=6\sqrt{2}$
respectively.

Now, $C_1{C}_2=\sqrt{{\left(6+3\right)}^2+{\left(6+3\right)}^2}$

$=9\sqrt{2}$

and $r_1+r_2=3\sqrt{2}+6\sqrt{2}=9\sqrt{2}$

$\Rightarrow C_1{C}_2=r_1+r_2$

$\therefore$ Both circles touch each other externally.