Question

The equation of an ex-circle of a triangle formed by the common tangents to the circle $x^{2}+y^{2}=4$ and $x^{2}+y^{2}-6x+8=0$ is

• A. $x^{2}+y^{2}=4$
• B. $x^{2}+y^{2}-6x+8=0$
• C. $x^{2}+y^{2}-6x+9=0$
• D. $x^{2}+y^{2}=1$

Answer 1

Answer: (A)

For $x^{2}+y^{2}=2^{2}$ , the centre is $\left(0 , 0\right)$ and radius is $2$ units
and for $x^{2}+y^{2}-6x+8=0$ , the centre is $\left(3 , 0\right)$ and radius is $1$ unit
Now, note that the circles touch each other externally, hence the larger circle is an excircle of the triangle formed by the common tangents.