Q84.If the minimum area of the triangle formed by a tangent to the ellipse x2 = 1 and the co-ordinate axis is + 4a2 b2 kab, then k is equal to ___________.
What This Question Tests
This question requires writing the equation of a tangent to an ellipse, finding its intercepts to form a triangle, and then minimizing the area of this triangle using calculus or algebraic methods.
Concepts Tested
Formulas Used
Tangent to x^2/a^2 + y^2/b^2 = 1 at (x1,y1): xx1/a^2 + yy1/b^2 = 1
Tangent with slope m: y = mx ± √(a^2m^2 + b^2)
Area of triangle with intercepts (X,0) and (0,Y) is 1/2 |X Y|
📚 NCERT Sections This Tests
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.)
9.15 — 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.
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.
📋 Question Details
- Chapter
- Applications of Derivatives
- Topic
- Tangent to Ellipse, Area of Triangle, Maxima and Minima
- Year
- 2021
- Shift
- 27 Aug Shift 1
- Q Number
- Q84
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections, Class 12 Mathematics Ch 6: Applications of Derivatives
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