Q71.Let the tangents drawn to the circle, x2 + y2 = 16 from the point P(0, h) meet the x -axis at points A and B . If the area of ΔAPB is minimum, then positive value of h is: (1) 4√2 (2) 3√2 (3) 4√3 (4) 3√3
What This Question Tests
This question combines finding the equation of tangents to a circle, calculating the area of a triangle formed by these tangents and the x-axis, and then using calculus to minimize this area.
Concepts Tested
Formulas Used
Equation of tangent to x²+y²=r² from (x1, y1) is x*x1+y*y1=r²
Area of triangle = 1/2 * base * height
Differentiation for minimization
📚 NCERT Sections This Tests
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.
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.)
2.2 — A Regular Hexagon Of Side 10 Cm Has A Charge 5 Mc At Each Of Its
Physics Class 11 · 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.
📋 Question Details
- Chapter
- Circles
- Topic
- Tangents to a circle
- Year
- 2015
- Shift
- 10 Apr Online
- Q Number
- Q71
- Type
- Multi concept
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections, Class 12 Mathematics Ch 6: Applications of Derivatives
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