Question

The number of common tangents to the circles $x^{2}+y^{2}=4$ and $x^{20}+y^{2}-6\,x-8\,y=24$ is

• A. $0$
• B. $1$
• C. $3$
• D. $4$

Answer 1

Answer: (B)

The centres of the given circles $x^2 + y^2 = 4$ and $x^2 + y^2 - 6\,x - 8\,y = 24$ are $C_1 (0, 0)$ and $C_2 (3, 4)$ respectively. Their radii are $r_1 = 2$ and $r_2 = 7$ respectively.
$C_1C_2 = 5 <$ sum of radii
But $C_1C_2 =$ difference of radii
Thus, the given circles touch each other internally.
Hence, number of common tangent is only one.