Q65.Let an ellipse πΈ: π₯2 + π¦2 = 1, π2 > π2, passes through 3 1 and has eccentricity 1 If a circle, centered at β 2, β3. π2 π2 2 focus πΉ( πΌ, 0 ) , πΌ> 0, of πΈ and radius β3, intersects πΈ at two points π and π, then ππ2 is equal to : (1) 8 (2) 4 3 3 16 (3) (4) 3 3
What This Question Tests
This question involves finding the equation of an ellipse from given points and eccentricity, determining the focus, and then finding the intersection points of the ellipse with a circle centered at the focus to calculate the distance PQ.
Concepts Tested
Formulas Used
x^2/a^2 + y^2/b^2 = 1
b^2 = a^2(1-e^2)
Focus = (ae, 0)
Distance formula
π NCERT Sections This Tests
2.1 β Two Charges 5 Γ 10β8 C And β3 Γ 10β8 C Are Located 16 Cm Apart. At
Physics Class 11 Β· Chapter 2
2.1 Two charges 5 Γ 10β8 C and β3 Γ 10β8 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 β A Regular Hexagon Of Side 10 Cm Has A Charge 5 Mc At Each Of Its
Physics Class 11 Β· 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 β (A) Sin IΒ’C = 1.44/1.68 Which Gives IΒ’C = 59Β°. Total Internal Reflection
Physics Class 12 Β· Chapter 9
9.17 (a) sin iΒ’c = 1.44/1.68 which gives iΒ’c = 59Β°. Total internal reflection takes place when i > 59Β° or when r < rmax = 31Β°. Now, (sin i /sin r max max ) = 1.68 , which gives imax ~ 60Β°. Thus, all incident rays of angles in the range 0 < i < 60Β° 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, iΒ’c = sinβ1(1/1.68) = 36.5Β°. Now, i = 90Β° will have r = 36.5Β° and iΒ’ = 53.5Β° which is greater than iΒ’c. Thus, all incident rays (in the range 53.5Β° < i < 90Β°) will suffer total internal reflections.
π Question Details
- Chapter
- Ellipse
- Topic
- Equation of ellipse, Eccentricity, Intersection of circle and ellipse
- Year
- 2021
- Shift
- 25 Jul Shift 1
- Q Number
- Q65
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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