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  • If two circles <img alt="\mathrm{(x-1)^2+(y-3)^2=r^2 \text { 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%3

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

Option: 1

\mathrm{2< r <8}


Option: 2

\mathrm{r<2}


Option: 3

\mathrm{r=2}


Option: 4

\mathrm{r>2}


Answers (1)

best_answer

Let d be the distance between the centres of two circles of radii r1
and \mathrm{r_2}.
These circle intersect at two distinct points if \mathrm{\left|r_1-r_2\right|<d<r_1+r_2}

Here, the radii of the two circles are r and 3 and distance between the centres is 5.
centres is 5.

Thus \mathrm{|r-3|<5 r+3 \Rightarrow-2<r<8 \text { and } r>2 \Rightarrow 2<r<8 \text {. }}

Hence (a) is the coorect answer.

Posted by

Ritika Kankaria

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