Q73.If the curves, x2 −6x + y2 + 8 = 0 and x2 −8y + y2 + 16 −k = 0, (k > 0) touch each other at a point, then the largest value of k is ____________. → → → → π If →a
What This Question Tests
This problem involves finding the centers and radii of two circles from their general equations and then applying the condition for two circles to touch externally or internally (distance between centers equals sum or difference of radii).
Concepts Tested
Formulas Used
(x-h)² + (y-k)² = r²
Distance between centers = |r1 ± r2|
📚 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.
2.2 — A Regular Hexagon Of Side 10 Cm Has A Charge 5 Mc At Each Of Its
Physics Class 11 · Chapter 2
2.2 A regular hexagon of side 10 cm has a charge 5 mC at each of its vertices. Calculate the potential at the centre of the hexagon.
9.17 — (A) Sin I¢C = 1.44/1.68 Which Gives I¢C = 59°. Total Internal Reflection
Physics Class 12 · Chapter 9
9.17 (a) sin i¢c = 1.44/1.68 which gives i¢c = 59°. Total internal reflection takes place when i > 59° or when r < rmax = 31°. Now, (sin i /sin r max max ) = 1.68 , which gives imax ~ 60°. Thus, all incident rays of angles in the range 0 < i < 60° will suffer total internal reflections in the pipe. (If the length of the pipe is finite, which it is in practice, there will be a lower limit on i determined by the ratio of the diameter to the length of the pipe.) (b) If there is no outer coating, i¢c = sin–1(1/1.68) = 36.5°. Now, i = 90° will have r = 36.5° and i¢ = 53.5° which is greater than i¢c. Thus, all incident rays (in the range 53.5° < i < 90°) will suffer total internal reflections.
📋 Question Details
- Chapter
- Circles
- Topic
- Condition for two circles to touch
- Year
- 2020
- Shift
- 09 Jan Shift 2
- Q Number
- Q73
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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