Circles
Number of Common Tangents to Two Circles
nta_pyq_2023_apr
Grade 11
Question:
The number of common tangents, to the circles $x^2+y^2-18x-15y+131=0$ and $x^2+y^2-6x-6y-7=0$, is
Step-by-Step Solution
Key Concept: Find centres and radii: $C_1=(9,\frac{15}{2}),\ r_1=\frac{5}{2}$; $C_2=(3,3),\ r_2=5$. Compare $d=|C_1C_2|$ with $r_1+r_2$ and $|r_1-r_2|$.
$d=\frac{15}{2},\ r_1+r_2=\frac{15}{2}$. External tangency $\Rightarrow 3$ common tangents.
Correct Answer: 1