Q66.The locus of the centroid of the triangle formed by any point ๐ on the hyperbola 16๐ฅ2 - 9๐ฆ2 + 32๐ฅ+ 36๐ฆ- 164 = 0 and its foci is (1) 16๐ฅ2 - 9๐ฆ2 + 32๐ฅ+ 36๐ฆ- 36 = 0 (2) 9๐ฅ2 - 16๐ฆ2 + 36๐ฅ+ 32๐ฆ- 144 = 0 (3) 16๐ฅ2 - 9๐ฆ2 + 32๐ฅ+ 36๐ฆ- 144 = 0 (4) 9๐ฅ2 - 16๐ฆ2 + 36๐ฅ+ 32๐ฆ- 36 = 0
What This Question Tests
The question requires converting the hyperbola equation to standard form to find its center and foci, then using the centroid formula for a point on the hyperbola and its foci to derive the locus.
Concepts Tested
Formulas Used
(x-h)^2/a^2 - (y-k)^2/b^2 = 1
Foci (h +/- ae, k)
Centroid = ((x1+x2+x3)/3, (y1+y2+y3)/3)
๐ NCERT Sections This Tests
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9.19 โ A Screen Is Placed 90Cm From An Object. The Image Of The Object On
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2.1 Two charges 5 ร 10โ8 C and โ3 ร 10โ8 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.
๐ Question Details
- Chapter
- Hyperbola
- Topic
- Equation of hyperbola, Foci, Centroid, Locus
- Year
- 2021
- Shift
- 25 Jul Shift 1
- Q Number
- Q66
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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