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

• Coordinate Geometry

If the two circles (x-1)² + (y-3)² = r² and x² + y² - 8x + 2y + 8 = 0 intersect in two distinct point, then

1. 2 < r < 8
2. r = 2
3. r > 2
4. r < 2

Answer

|r₁ - r₂| = C₁ C₂ for intersection

⇒ r - 3 < 5

⇒ r < 8 ......... (1)

and r₁ + r₂ > C₁ C₂

⇒ r + 3 > 5

⇒ r > 2 ......... (2)

From (1) and (2), 2 < r < 8.

The correct option is A.