The locus of the centroid of the triangle formed by any poi…

Maths Conic Sections JEE Main 2021 - ( Hyperbola ) Single Correct MCQ

Published on: August 14, 2026

The locus of the centroid of the triangle formed by any point P on the hyperbola 16x 2 − 9y 2 + 32x + 36y − 164 = 0, and its foci is :

16x 2 − 9y 2 + 32x + 36y − 36 = 0

9x 2 − 16y 2 + 36x + 32y − 144 = 0

16x 2 − 9y 2 + 32x + 36y − 144 = 0

9x 2 − 16y 2 + 36x + 32y − 36 = 0

Text Solution

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The correct answer is:

Given hyperbola is 16(x + 1) 2 − 9(y − 2) 2 = 164 + 16 − 36 = 144

Eccentricity,

⇒ foci are (4, 2) and (−6, 2)

Let the centroid be (h, k)

\&A(α, β) be point on hyperbola

⇒ α = 3 h + 2, β = 3k − 4

(α, β) lies on hyperbola so 16(3 h + 2 + 1) 2 − 9(3k − 4 − 2) 2 = 144

⇒ 144( h + 1) 2 − 81(k − 2) 2 = 144

⇒ 16 (h 2 + 2h + 1) − 9 (k 2 − 4k + 4) = 16

⇒ 16x 2 − 9y2+ 32x + 36y − 36 = 0

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