Question

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

• A. 0
• B. 1
• C. 3
• D. 4

Answer 1

Answer: (B)

1

Answer 2

Circles $S _ { 1 } \equiv x ^ { 2 } + y ^ { 2 } = ( 2 ) ^ { 2 }$ and

$\therefore$

Centres $C _ { 2 } = ( 3,4 )$ and radii $r _ { 2 } = 7$

$C _ { 1 } C _ { 2 } = \sqrt { ( 3 ) ^ { 2 } + ( 4 ) ^ { 2 } } = 5$, $r _ { 2 } - r _ { 1 } = 7 - 2 = 5$

$\therefore$ $C _ { 1 } C _ { 2 } = r _ { 2 } - r _ { 1 }$ i.e. circles touch internally.

Hence there is only one common tangent.