Question

The circles $x^2+y^2+4x-2y+4=0$ and $x^2+y^2-2x-4y-20=0$

• A. intersect each other.
• B. touch each other externally.
• C. touch each other internally.
• D. are such that one circle lies entirely inside another circle.

Answer 1

Answer: (D)

are such that one circle lies entirely inside another circle.

$x^2+y^2+4x-2y+4=0$ [ From point (1) ]
$C_1\equiv (-2,1)$
$r_1=1$
and $x^2+y^2-2x-4y-20=0$
$C_2\equiv (1,2)$
$r_2=5$
$\therefore$ distance $be{t}^n$ centre $=\sqrt{(3{)}^2+(1{)}^2}$
$=\sqrt{10}$
$r_1+r_2=6>\sqrt{10}$ ...... $\left(1\right)$
and $r_2-r_1=4>\sqrt{10}$ ..... $\left(2\right)$
From (1) and (2)
Given two circles are such that the circle lies entirely inside another.