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Question: If the circles x<sup>2</sup> + y<sup>2</sup> = 9 and x<sup>2</sup> + y<sup>2</sup> + 2ax + 2y +1 = 0...

If the circles x2 + y2 = 9 and x2 + y2 + 2ax + 2y +1 = 0 touches each other then a :

A

0

B

1

C

–43\frac { 4 } { 3 }

D

– 34\frac { 3 } { 4 }

Answer

–43\frac { 4 } { 3 }

Explanation

Solution

c1(0, 0) , r1 = 3 & c2(–a,–1), r2 = |a|

Circles touches each other if c1c2 = r1 ± r2

α2+1\sqrt { \alpha ^ { 2 } + 1 } = 3 ± |a|

a2 + 1 = 9 + a2 ± 6|a|

6|a| = ± 8

a = ± 43\frac { 4 } { 3 }