Q72.Let A(4, −4) and B(9, 6) be points on the parabola, y2 = 4x. Let C be chosen on the arc AOB of the parabola, where O is the origin, such that the area of ΔACB is maximum. Then, the area (in sq. units) of ΔACB , is: (1) 32 (2) 31 34 (3) 30 12 (4) 31 14
What This Question Tests
This multi-concept question requires maximizing the area of a triangle with two fixed vertices and the third on a parabola, by finding a point where the tangent is parallel to the base using differential calculus.
Concepts Tested
Formulas Used
Area = (1/2) |x₁ (y₂ - y₃) + x₂ (y₃ - y₁) + x₃ (y₁ - y₂)|
Derivative dy/dx for y²=4x
Tangent parallel to base for maximum area
📚 NCERT Sections This Tests
9.15 — Apply Mirror Equation And The Condition:
Physics Class 12 · Chapter 9
9.15 Apply mirror equation and the condition: (a) f < 0 (concave mirror); u < 0 (object on left) (b) f > 0; u < 0 (c) f > 0 (convex mirror) and u < 0 (d) f < 0 (concave mirror); f < u < 0 to deduce the desired result.
9.5 — A Small Bulb Is Placed At The Bottom Of A Tank Containing Water To A
Physics Class 12 · Chapter 9
9.5 A small bulb is placed at the bottom of a tank containing water to a depth of 80cm. What is the area of the surface of water through which light from the bulb can emerge out? Refractive index of water is 1.33. (Consider the bulb to be a point source.)
9.18 — For Fixed Distance S Between Object And Screen, The Lens Equation
Physics Class 12 · Chapter 9
9.18 For fixed distance s between object and screen, the lens equation does not give a real solution for u or v if f is greater than s/4. Therefore, fmax = 0.75 m.
📋 Question Details
- Chapter
- Parabola
- Topic
- Area of triangle, Maximization
- Year
- 2019
- Shift
- 09 Jan Shift 2
- Q Number
- Q72
- Type
- Multi concept
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections, Class 12 Mathematics Ch 6: Applications of Derivatives
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