Q72.If the tangent at a point on the ellipse x2 27 + 3 = 1 meets the coordinate axes at A and B, and O is the origin, then the minimum area (in sq. units) of the triangle OAB is (1) 3√3 (2) 92 (3) 9 (4) 9√3
What This Question Tests
This problem requires finding the equation of a tangent to an ellipse, determining its intercepts with the coordinate axes, and then minimizing the area of the triangle formed using either calculus or AM-GM inequality.
Concepts Tested
Formulas Used
x x1/a^2 + y y1/b^2 = 1
Area = 1/2 |x_int * y_int|
📚 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.
12.7 — The Radius Of The Innermost Electron Orbit Of A Hydrogen Atom Is
Physics Class 12 · Chapter 12
12.7 The radius of the innermost electron orbit of a hydrogen atom is 5.3×10–11 m. What are the radii of the n = 2 and n =3 orbits?
📋 Question Details
- Chapter
- Ellipse
- Topic
- Tangent to an ellipse
- Year
- 2016
- Shift
- 09 Apr Online
- Q Number
- Q72
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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