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  • The number of common tangents to the circle and <img alt="\mathrm{x^2+

The number of common tangents to the circle \mathrm{x^2+y^2=4} and \mathrm{x^2+y^2-2 y-3=0} is
 

Option: 1

1


Option: 2

2


Option: 3

3


Option: 4

4


Answers (1)

best_answer

 Given  \mathrm{x^2+y^2=4 } and  \mathrm{x^2+(y-1)^2=4}

\begin{aligned} & \mathrm{ \Rightarrow \quad r_1=2, r_2=2, r_1+r_2=4 \Rightarrow C_1 \equiv(0,0), C_2 \equiv(0,1) }\\ & \mathrm{\therefore C_1 C_2=1} \\ & \mathrm{\therefore \quad\left|r_1-r_2\right|<\left|C_1 C_2\right|<r_1+r_2 }\end{aligned}
\therefore Then two given circles are intersecting circle.
\therefore There are two direct common tangents.

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Ritika Kankaria

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