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  • The number of common tangents of the circles <img alt="\mathrm{(x+2)^2+(y-2)^2=49 \: and\: (x-2)^2+(y+1)^2=4}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%28x&plus;2%29%5E

The number of common tangents of the circles \mathrm{(x+2)^2+(y-2)^2=49 \: and\: (x-2)^2+(y+1)^2=4} is
 

Option: 1

0


Option: 2

1


Option: 3

3


Option: 4

4


Answers (1)

best_answer

The given circles have centre at

\mathrm{C_1(-2,2), C_2(2,-1)\: and\: \: radii \: \: r_1=7, r_2=2}

Now \mathrm{C_1 C_2=\sqrt{(2+2)^2+(-1-2)^2}=\sqrt{16+9}=5=r_1-r_2}

\therefore  given circles touch internally.

\therefore  there is only one common tangent.

Hence option 2 is correct.

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