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The two circles \mathrm{x^{2}+y^{2}-2 x-3=0} and \mathrm{x^{2}+y^{2}-4 x-6 y-8=0} are such that
 

Option: 1

 they touch each other


Option: 2

 they intersect each other


Option: 3

one lies inside the other


Option: 4

each lies outside the other


Answers (1)

best_answer

The coordinates of centres \mathrm{C}_{1} and \mathrm{C}_{2} of two circles are (1,0) and (2,3) respectively. Let \mathrm{r}_{1} and \mathrm{r}_{2} be

the radii of two circles. Then \mathrm{r}_{1}=2 and \mathrm{r}_{2}=\sqrt{21}.\mathrm{Clearly \: \mathrm{r}_{1}-\mathrm{r}_{2}<\mathrm{c}_{1} \mathrm{c}_{2}<\mathrm{r}_{1}+\mathrm{r}_{2}}

Hence the two circles intersect each other.

Posted by

jitender.kumar

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