Question

Consider the circles $x^2+(y-1)^2=9,(x-1)^2+y^2=25$. They are such that-

• A. each of these circles lies outside the other
• B. one of these circles lies entirely inside the other
• C. these circles touch each other
• D. they intersect in two points

Answer 1

Answer: (B)

$C_1(0,1), r_1=3$
$C_2(1,0), r_2=5$
$C_1 C_2=\sqrt{2}$
$\left|r_1-r_2\right|=2$
$\Rightarrow c_1 c_2<\left|r_1-r_2\right|$