Q71.If a variable line 3x + 4y −λ = 0 is such that the two circles x2 + y2 −2x −2y + 1 = 0 and x2 + y2 −18x −2y + 78 = 0 are on its opposite sides, then the set of all values of λ is the interval : (1) [13, 23] (2) (23, 31) (3) [12, 21] (4) (2, 17)
What This Question Tests
This question tests the concept of determining whether two points (or in this case, centers of circles) lie on opposite sides of a line. For two points to be on opposite sides of the line ax+by+c=0, the values of ax+by+c when substituting the coordinates of the points must have opposite signs. Determine the centers of the two circles and apply this condition to find the range of λ.
Concepts Tested
Formulas Used
Equation of circle (x-h)^2 + (y-k)^2 = r^2
Sign of L(x,y) for a point (x,y) relative to line L=0
📚 NCERT Sections This Tests
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.
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)]+
2.4 — A Spherical Conductor Of Radius 12 Cm Has A Charge Of 1.6 × 10–7C
Physics Class 11 · Chapter 2
2.4 A spherical conductor of radius 12 cm has a charge of 1.6 × 10–7C distributed uniformly on its surface. What is the electric field (a) inside the sphere (b) just outside the sphere (c) at a point 18 cm from the centre of the sphere?
📋 Question Details
- Chapter
- Circles
- Topic
- Relative position of a line and circles
- Year
- 2019
- Shift
- 12 Jan Shift 1
- Q Number
- Q71
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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