First slide

Analysis of two circles in circles

Question

The two circles $x^{2} + y^{2} - 2 x - 3 = 0$ and $x^{2} + y^{2} - 46 y - 8 = 0$ are such that

Easy

A

They touch each other
B

They intersect each other
C

One lies inside the other
D

Each lies outside the other.

Solution

The two circles are $x^{2} + y^{2} - 2 x - 3 = 0$ and $x^{2} + y^{2} - 4 x - 6 y - 8 = 0$ . $C' (2, 3)$ respectively and their radii are 2 and $\sqrt{21}$ respectively, Here,
$| C C' | = \sqrt{{(2 - 1)}^{2} + {(3 - 0)}^{2}} = \sqrt{10}$

Since $| 2 - \sqrt{21} | < | C C' | < 2 + \sqrt{21}$ .

Therefore, the two circles interest in two distinct points

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