JEE AdvancedCircleHard
Question
If the two circles (x -1)2 + ( y - 3)2 = r2 and x2 + y2 -8x + 2y + 8 = 0 intersect in two distinct points. then
Options
A.2 < r < 8
B.r < 2
C.r = 2
D.r > 2
Solution
As, the two circles intersect in two distinct points.
⇒ distance between centres lies between |r1 - r2| and |r1 + r2|
ie,
⇒ |r - 3 | < 5 < | r + 3 |
⇒ r < 8 or r > 2
∴ 2 < r < 8
⇒ distance between centres lies between |r1 - r2| and |r1 + r2|
ie,
⇒ |r - 3 | < 5 < | r + 3 |
⇒ r < 8 or r > 2
∴ 2 < r < 8
Create a free account to view solution
View Solution FreeMore Circle Questions
Let A and B be two distinct points on the parabola y2 = 4x. If the axis of the parabola touches a circle of radius r hav...The equation of the circle passing through (1, 1) and the points of intersection of x2 + y2 + 13x - 3y = 0 and 2x2 + 2y2...The locus of the point z which moves such that 2 arg = π is -...The locus of the mid-points of the chords of the circle x2 + y2 - 2x - 4y - 11 = 0 which subtend 60o at the centre is -...Identify the correct statement(s) -...