Q68.Let a circle of radius 4 be concentric to the ellipse 15𝑥2 + 19𝑦2 = 285. Then the common tangents are inclined to the minor axis of the ellipse at the angle (1) π (2) π 3 4 π π (3) (4) 6 12
What This Question Tests
The question tests the ability to find common tangents to a circle and an ellipse by equating the tangent conditions and then determining the angle these tangents make with the minor axis.
Concepts Tested
Formulas Used
y = mx ± sqrt(a^2m^2 + b^2)
y = mx ± r sqrt(1+m^2)
Angle with axes
📚 NCERT Sections This Tests
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.
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?
6.11 — Dynamics Of Rotational
Physics Class 11 · Chapter 6
6.11 Dynamics of rotational the motion of extended bodies. motion about a fixed axis A large class of problems with extended bodies can be
📋 Question Details
- Chapter
- Ellipse
- Topic
- Common tangents of circle and ellipse
- Year
- 2023
- Shift
- 10 Apr Shift 2
- Q Number
- Q68
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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