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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}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bx%5E2&plus;y%5E

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

\mathrm{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 \text { and } x^2+y^2+2 x+2 y+1=0}

Centre : \mathrm{\mathrm{C}_1 \equiv(2,3), \mathrm{C}_2 \equiv(-1,-1)}  radii : \mathrm{ \mathrm{r}_1=4, \mathrm{r}_2=1}

We have  \mathrm{\mathrm{C}_1 \mathrm{C}_2=5=\mathrm{r}_1+\mathrm{r}_2} , therefore there are 3 common tangents to the given circles.

Hence (c) is correct answer.

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mansi

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