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  • The number of common tangents that can be drawn to the circle <img alt="\mathrm{x^{2}+y^{2}-4 x-6 y-3=0\: and \: x^{2}+y^{2}+2 x+2 y+1=0}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cma

The number of common tangents that can be drawn to the circle \mathrm{x^{2}+y^{2}-4 x-6 y-3=0\: and \: x^{2}+y^{2}+2 x+2 y+1=0} is

Option: 1

1


Option: 2

2


Option: 3

3


Option: 4

4


Answers (1)

best_answer

The two circles are \mathrm{x^{2}+y^{2}-4 x-6 y-3=0\: and \: x^{2}+y^{2}+2 x+2 y+1=0}
Centre: \mathrm{C_{1} \equiv(2,3), C_{2} \equiv(-1,-1) }
\mathrm{radii: r_{1}=4, r_{2}=1 }

We have, \mathrm{C_{1} C_{2}=5=r_{1}+r_{2}}, therefore there are 3 common tangents to the given circles.

Hence (C) is the correct answer.


 

 

Posted by

Ritika Harsh

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