Q57.If the point P on the curve, 4x2 + 5y2 = 20 is farthest from the point Q(0, −4), then PQ2 is equal to (1) 36 (2) 48 (3) 21 (4) 29
What This Question Tests
This problem involves setting up the square of the distance from a point on an ellipse to a fixed point, expressing it in terms of a single variable, and then using calculus (differentiation) to find the maximum distance.
Concepts Tested
Formulas Used
Distance formula D^2 = (x2-x1)^2 + (y2-y1)^2
Derivative for extrema d(D^2)/dy = 0
📚 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.
9.15 — 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.
2.4 — A Spherical Conductor Of Radius 12 Cm Has A Charge Of 1.6 × 10–7C
Physics Class 11 · Chapter 2
2.4 A spherical conductor of radius 12 cm has a charge of 1.6 × 10–7C distributed uniformly on its surface. What is the electric field (a) inside the sphere (b) just outside the sphere (c) at a point 18 cm from the centre of the sphere?
📋 Question Details
- Chapter
- Applications of Derivatives
- Topic
- Maxima and Minima (finding extreme distance)
- Year
- 2020
- Shift
- 05 Sep Shift 1
- Q Number
- Q57
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections; Class 12 Mathematics Ch 6: Applications of Derivatives
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