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The two circles x^2+y^2=ax and x^2+y^2=c...

The two circles `x^2+y^2=ax and x^2+y^2=c^2(c > 0)` touch each other if (1) `a=2c` (2) `|a|=2c` (3) `2|a|=c` (4) `|a|=c`

A

`|a| = 2c`

B

`2 |a| =c`

C

` | a| =c`

D

`a = 2c`

Text Solution

Verified by Experts

The correct Answer is:
3

The figure is self-explanatory, Clearly `c= |a|`
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Statement 1 :The circles x^2+y^2+2p x+r=0 and x^2+y^2+2q y+r=0 touch if 1/(p^2)+1/(q^2)=1/r dot Statement 2 : Two centers C_1a n dC_2 and radii r_1a n dr_2, respectively, touch each other if |r_1+-r_2|=c_1c_2dot