Home
Class 12
MATHS
Two circles centres A and B radii r1 and...

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. circles `x^2 + y^2 + 2ax + c^2 = 0 and x^2 + y^2 + 2by + c^2 = 0` touche each other if (A) `1/a^2 + 1/b^2 = 2/c^2` (B) `1/a^2 + 1/b^2 = 2/c^2` (C) `1/a^2 - 1/b^2 = 2/c^2` (D) `1/a^2 - 1/b^2 = 4/c^2`

Promotional Banner

Similar Questions

Explore conceptually related problems

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. Number of common tangents to the circles x^2 + y^2 - 6x = 0 and x^2 + y^2 + 2x = 0 is (A) 1 (B) 2 (C) 3 (D) 4

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

The distance between the centres of the two circles of radii r_1 and r_2 is d. They will thouch each other internally if

Two circles of radii r_(1) and r_(2), r_(1) gt r_(2) ge2 touch each other externally. If theta be the angle between the direct common tangents, then,

Two circles with centres C_(1),C_(2) and same radius r cut each other orthogonally,then r is

Two fixed circles with radii r_(1) and r_(2),(r_(1)>r_(2)), respectively,touch each other externally.Then identify the locus of the point of intersection of their direction common tangents.

Two circle with radii r_(1) and r_(2) respectively touch each other externally. Let r_(3) be the radius of a circle that touches these two circle as well as a common tangents to two circles then which of the following relation is true

The circles having radii r1 and r2 intersect orthogonally Length of their common chord is

Two circles of radius 1 and 4 touch each other externally.Another circle of radius r touches both circles externally and also one direct common tangent of the two circles.Then [(1)/(r)]=