Q82.If the circles x2 + y2 + 6x + 8y + 16 = 0 and x2 + y2 + 2(3 −√3)x 2(4 −√6)y 2 2 + + + k > 0 , touch internally at the point P(α, β), then (α √3) (β √6) is equal to _______.
What This Question Tests
This question tests the understanding of properties of circles, specifically internal tangency, requiring the calculation of centers and radii, and then finding the point of contact using section formula or geometric properties.
Concepts Tested
Formulas Used
Center (-g, -f) and radius sqrt(g^2 + f^2 - c) from x^2 + y^2 + 2gx + 2fy + c = 0
Distance between centers C1C2 = |r1 - r2| for internal tangency
Point of contact P divides C1C2 in ratio r1:r2 externally or r1:r2 internally on line of centers
📚 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.
2.2 — 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.
2.5 — A Parallel Plate Capacitor With Air Between The Plates Has A
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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?
📋 Question Details
- Chapter
- Circles
- Topic
- Touching circles
- Year
- 2022
- Shift
- 25 Jul Shift 2
- Q Number
- Q82
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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