Question
Question: If two circles (x-1)<sup>2</sup>+(y-3)<sup>2</sup> = r<sup>2</sup> and x<sup>2</sup>+y<sup>2</sup>-8...
If two circles (x-1)2+(y-3)2 = r2 and x2+y2-8x+2y+8 = 0 intersect in two distinct points then
A
2 < r < 8
B
r < 2
C
r = 2
D
r > 2
Answer
2 < r < 8
Explanation
Solution
Let d be the distance between the centres of two circles of radii r1 and r2 .These circle intersect at two distinct points if r1-r2 < d < r1+r2.
Here, the radii of the two circles are r and 3 and distance between the centres is 5.
Thus, r-3 < 5 < r+3
⇒ -2 < r < 8 and r > 2 ⇒ 2 < r < 8