Question

The coordinates of the point at which the circles $x^2+y^2-4x-2y-4=0$ and $x^2+y^2-12x-8y-36=0$ touch each other, are

• A. $(3,-2)$
• B. $(-2,3)$
• C. $(3,2)$
• D. None of these

Answer 1

The correct option is D None of these

Given circles are

$x^2+y^2-4x-2y-4=0$ ...(1)

and $x^2+y^2-12x-8y-36=0$ ...(2)

Center of circle (1) is $C_1\equiv (2,1)$ and radius $=r_1=\sqrt{4+1+4}=3$

Center of circle (2) is $C_2\equiv (6,4)$ and radis $=r_2=\sqrt{36+16+36}=\sqrt{88}$

Also, $d=$ distance $C_1$ and $C_2$

$=C_1{C}_2=\sqrt{16+9}=5$

Since $d\ne r_1\pm r_2$

$\therefore$ the two circles do not touch each other.