Q71.Let P be the point on the parabola, y2 = 8x which is at a minimum distance from the center C of the circle x2 + (y + 6)2 = 1. Then the equation of the circle, passing through C and having its center at P is (1) x2 + y2 −x4 + 2y −24 = 0 (2) x2 + y2 −4x + 9y + 18 = 0 (3) x2 + y2 −4x + 8y + 12 = 0 (4) x2 + y2 −x + 4y −12 = 0
What This Question Tests
This multi-concept question requires finding a point on a parabola closest to a given point (center of another circle) using calculus, and then using this point as the center of a new circle passing through the initial center.
Concepts Tested
Formulas Used
y^2 = 4ax
Distance formula
d(f(t))/dt = 0
(x-h)^2 + (y-k)^2 = r^2
📚 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.
2.5 — A Parallel Plate Capacitor With Air Between The Plates Has A
Physics Class 11 · Chapter 2
2.5 A parallel plate capacitor with air between the plates has a capacitance of 8 pF (1pF = 10–12 F). What will be the capacitance if the distance between the plates is reduced by half, and the space between them is filled with a substance of dielectric constant 6?
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
- Parabola
- Topic
- Minimum distance and equation of circle
- Year
- 2016
- Shift
- 03 Apr
- Q Number
- Q71
- Type
- Multi concept
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections AND Class 12 Mathematics Ch 6: Applications of Derivatives
More from this Chapter
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