Coordinate Geometry
Sum of lengths of common tangents
Grade Class 12
Question:
Sum of length of all the common tangents of the circles $x^2+y^2-2x-8y+15=0$ and $x^2+y^2-6x-12y+43=0$ is
$\sqrt{2}$
$2\sqrt{2}$
$4\sqrt{2}$
$5\sqrt{2}$
Step-by-Step Solution
Key Concept: Circle 1: centre $(1,4)$, $r=\sqrt{2}$. Circle 2: centre $(3,6)$, $r=\sqrt{2}$. Distance $d=2\sqrt{2}=r_1+r_2$: circles are externally tangent.
Sum $=4\sqrt{2}$.
Correct Answer: 3