First slide

Analysis of two circles in circles

Question

The two circles $x^{2} + y^{2} - 5 = 0$ and $x^{2} + y^{2} - 2 x - 4 y - 15 = 0$

Moderate

A

touch each other externally
B

touch each other internally
C

cut each other orthogonally
D

do not intersect

Solution

Coordinates of the centres of the two circles are $C_{1} (0, 0), C_{2} (1, 2)$ and their radii are $r_{1} = \sqrt{5}, r_{2} = 2 \sqrt{5}$ .
We have, $C_{1} C_{2} = \sqrt{5} = r_{2} - r_{1} .$
Hence, the two circles touch each other internally.

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App