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  • If the two circles <img alt="\mathrm{(x-1)^2+(y-3)^2=r^2\: and \: x^2+y^2-8 x+2 y+8=0}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%28x-1%29%5E2&plus;%28y-3%29%5E2%3Dr%5E2

If the two circles \mathrm{(x-1)^2+(y-3)^2=r^2\: and \: x^2+y^2-8 x+2 y+8=0} intersect in two distinct points, then
 

Option: 1

2<\mathrm{r}<8

 


Option: 2

\mathrm{r<2}
 


Option: 3

\mathrm{r=2}
 


Option: 4

\mathrm{r>2}


Answers (1)

best_answer


The radii of the circles are \mathrm{r \: and \: 3} . The distance between the centres \mathrm{=5}

\mathrm{\Rightarrow r+3>5 \quad\quad \Rightarrow r>2 }

\mathrm{\text { Also } r-3<5 \quad \Rightarrow r<8 \quad \Rightarrow 2<r<8 }

Hence option 1 is correct.






 

Posted by

Divya Prakash Singh

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