If the two circles $${(x - 1)^2}\, + \,{(y - 3)^2} = \,{r^2}$$ and $$\,{x^2}\, + \,{y^2} - \,8x\, + \,2y\, + \,\,8\,\, = 0$$ intersect in two distinct point, then :
JEE · Math · previous-year question
- A.$$r > 2$$
- B.$$2 < r < 8$$correct
- C.$$r < 2$$
- D.$$r = 2.$$
Answer
B. $$2 < r < 8$$
Explanation
$$\left| {{r_1} - {r_2}} \right| < {C_1}{C_2}$$ for intersection $$ \Rightarrow r - 3 < 5 \Rightarrow r < 8\,\,\,\,\,\,\,\,\,...\left( 1 \right)$$ and $${r_1} + {r_2} > {C_1}{C_2},\,$$ $$r + 3 > 5 \Rightarrow r > 2\,\,\,...\left( 2 \right)$$ From $$\left( 1 \right)$$ and $$\left( 2 \right),$$ $$2 < r < 8.$$
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