Q69.The tangent to the parabola 𝑦2 = 4𝑥 at the point where it intersects the circle 𝑥2 + 𝑦2 = 5 in the first quadrant, passes through the point: (1) 1 3 (2) -1 4 4, 4 3, 3 1 1 3 7 (3) - 4, 2 (4) 4, 4
What This Question Tests
The question requires finding the point of intersection between a parabola and a circle in the first quadrant, then determining the equation of the tangent to the parabola at that point, and finally checking which given point lies on this tangent.
Concepts Tested
Formulas Used
Equation of parabola y^2=4ax
Equation of circle x^2+y^2=r^2
Equation of tangent to y^2=4ax at (x1,y1): y y1 = 2a(x+x1)
📚 NCERT Sections This Tests
2.1 — Two Charges 5 × 10–8 C And –3 × 10–8 C Are Located 16 Cm Apart. At
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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.
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Physics Class 12 · Chapter 9
9.8 A beam of light converges at a point P. Now a lens is placed in the path of the convergent beam 12cm from P. At what point does the beam converge if the lens is (a) a convex lens of focal length 20cm, and (b) a concave lens of focal length 16cm?
9.17 — (A) Sin I¢C = 1.44/1.68 Which Gives I¢C = 59°. Total Internal Reflection
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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
- Parabola
- Topic
- Intersection of parabola and circle, tangent to parabola
- Year
- 2019
- Shift
- 08 Apr Shift 2
- Q Number
- Q69
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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