If A and B are the points of intersection of the circle x² + y² - 8x = 0 and the hyperbola (x²)/9 - (y²)/4 = 1 and a point P moves on the line 2x - 3y + 4 = 0, then the centroid of PAB lies on the line:

Coordinate Geometry: JEE Main 2025 Mathematics question

JEE Main 2025 · January, Unspecified (session-level dataset) · Q89

JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumCoordinate Geometry478× since 2002

A

and

B

are the points of intersection of the circle

x^2 + y^2 - 8x = 0

and the hyperbola

\frac{x^2}{9} - \frac{y^2}{4} = 1

and a point

P

moves on the line

2x - 3y + 4 = 0

, then the centroid of

\triangle PAB

lies on the line: