Q69.The set of all real values of λ for which exactly two common tangents can be drawn to the circles x2 + y2 −4x −4y + 6 = 0 and x2 + y2 −10x −10y + λ = 0 is the interval: (1) (12, 32) (2) (18, 42) (3) (12, 24) (4) (18, 48)
What This Question Tests
This question requires finding the centers and radii of two circles and then applying the conditions for exactly two common tangents based on the distance between their centers and their radii.
Concepts Tested
Formulas Used
(x-h)²+(y-k)²=r²
Distance between centers d = √((h₂-h₁)²+(k₂-k₁)²)
Conditions for common tangents (d=|r₁-r₂| for 3, d>r₁+r₂ for 4, d<|r₁-r₂| for 0, d=r₁+r₂ for 3, |r₁-r₂|<d<r₁+r₂ for 2)
📚 NCERT Sections This Tests
5.11 — Draw All The Isomers (Geometrical And Optical) Of:
Chemistry Class 11 · Chapter 5
5.11 Draw all the isomers (geometrical and optical) of: (i) [CoCl2(en)2] + (ii) [Co(NH3)Cl(en)2] 2+ (iii) [Co(NH3)2Cl2(en)]+
5.12 — Write All The Geometrical Isomers Of [Pt(Nh3)(Br)(Cl)(Py)] And How Many Of
Chemistry Class 11 · Chapter 5
5.12 Write all the geometrical isomers of [Pt(NH3)(Br)(Cl)(py)] and how many of these will exhibit optical isomers?
2.1 — Two Charges 5 × 10–8 C And –3 × 10–8 C Are Located 16 Cm Apart. At
Physics Class 11 · Chapter 2
2.1 Two charges 5 × 10–8 C and –3 × 10–8 C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
📋 Question Details
- Chapter
- Circles
- Topic
- Common tangents to circles
- Year
- 2014
- Shift
- 11 Apr Online
- Q Number
- Q69
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections (circles part)
More from this Chapter
Q94.Consider a family of circles which are passing through the point (−1, 1) and are tangent to x− axis. If (h, k) are the co-ordinates of the centre of the circles, then the set of values of k is given by the interval (1) 0 < k < 1/2 (2) k ≥1/2 (3) −1/2 ≤k ≤1/2 (4) k ≤1/2
Q79.The point diametrically opposite to the point P(1, 0) on the circle x2 + y2 + 2x + 4y −3 = 0 is (1) (3, −4) (2) (−3, 4) (3) (−3, −4) (4) (3, 4)
Q67.Three distinct points A, B and C are given in the 2 - dimensional coordinate plane such that the ratio of the distance of any one of them from the point (1, 0) to the distance from the point (−1, 0) is equal to 31 . Then the circumcentre of the triangle ABC is at the point JEE Main 2009 JEE Main Previous Year Paper (1) (0, 0) (2) ( 54 , 0) (3) ( 25 , 0) (4) ( 53 , 0)
Q68.If P and Q are the points of intersection of the circles x2 + y2 + 3x + 7y + 2p −5 = 0 and x2 + y2 + 2x + 2y −p2 = 0, then there is a circle passing through P, Q and (1, 1) for (1) all values of p (2) all except one value of p (3) all except two values of p (4) exactly one value of p