Circle And System Of Circles Question 286
Question: If two circles $ {{(x-1)}^{2}}+{{(y-3)}^{2}}=r^{2} $ and $ x^{2}+y^{2}-8x+2y+8=0 $ intersect in two distinct points, then
[IIT 1989; Karnataka CET 2002; DCE 2000, 01; AIEEE 2003; MP PET 2004]
Options:
A) $ 2<r<8 $
B) $ r=2 $
C) $ r<2 $
D) $ r>2 $
Show Answer
Answer:
Correct Answer: A
Solution:
When two circles intersect each other, then
Difference between their radii $ \lt $ Distance between centers
$ \Rightarrow r-3<5\Rightarrow r=8 $ …..(i)
Sum of their radii > Distance between centres …..(ii)
$ \Rightarrow $ $ r+3>5\Rightarrow r>2 $
Hence by (i) and (ii), $ 2<r<8 $
BETA
