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 `:`

If the two circles (x-2)^(2)+(y+3)^(2) =lambda^(2) and x^(2)+y^(2) -4x +4y-1=0 intersect in two distinct points then :

Two circles centres A and B radii r_1 and r_2 respectively. (i) touch each other internally iff |r_1 - r_2| = AB . (ii) Intersect each other at two points iff |r_1 - r_2| ltAB lt r_1+ r_2 . (iii) touch each other externally iff r_1 + r_2 = AB . (iv) are separated if AB gt r_1 + r_2 . Number of common tangents to the two circles in case (i), (ii), (iii) and (iv) are 1, 2, 3 and 4 respectively. If circles (x-1)^2 + (y-3)^2 = r^2 and x^2 + y^2 - 8x + 2y + 8=0 intersect each other at two different points, then : (A) 1ltrlt5 (B) 5ltrlt8 (C) 2ltrlt8 (D) none of these

If the two circles (x+1)^2+(y-3)^2=r^2 and x^2+y^2-8x+2y+8=0 intersect at two distinct point,then (A) r > 2 (B) 2 < r < 8 (C) r < 2 (D) r=2

The two circles x^2+ y^2=r^2 and x^2+y^2-10x +16=0 intersect at two distinct points. Then

The two circles x^(2)+y^(2)-2x-2y-7=0 and 3(x^(2)+y^(2))-8x+29y=0

If the circles x^2+y^2+2ax+cy+a=0 and x^2+y^2-3ax+dy-1=0 intersect in two distinct points P and Q then show that the line 5x+6y-a=0 passes through P and Q for no value of a.

The two circles x^(2)+y^(2)-2x-3=0 and x^(2)+y^(2)-4x-6y-8=0 are such that

STATEMENT-1 : Let x^(2) + y^(2) = a^(2) and x^(2) + y^(2) - 6x - 8y -11 = 0 be two circles. If a = 5 then two common tangents are possible. and STATEMENT-2 : If two circles are intersecting then they have two common tangents.

Prove that the circles x^(2) +y^(2) - 4x + 6y + 8 = 0 and x^(2) + y^(2) - 10x - 6y + 14 = 0 touch at the point (3,-1)

If the circle x^2+y^2-4x-8y-5=0 intersects the line 3x-4y=m at two distinct points, then find the values of mdot