jee-main 2025 Q14

jee-main · India · session1_28jan_shift2 Conic sections Circle-Conic Interaction with Tangency or Intersection

If $A$ and $B$ are the points of intersection of the circle $x ^ { 2 } + y ^ { 2 } - 8 x = 0$ and the hyperbola $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 4 } = 1$ and a point P moves on the line $2 x - 3 y + 4 = 0$, then the centroid of $\triangle \mathrm { PAB }$ lies on the line :
(1) $x + 9 y = 36$
(2) $4 x - 9 y = 12$
(3) $6 x - 9 y = 20$
(4) $9 x - 9 y = 32$

If $A$ and $B$ are the points of intersection of the circle $x ^ { 2 } + y ^ { 2 } - 8 x = 0$ and the hyperbola $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 4 } = 1$ and a point P moves on the line $2 x - 3 y + 4 = 0$, then the centroid of $\triangle \mathrm { PAB }$ lies on the line :\\
(1) $x + 9 y = 36$\\
(2) $4 x - 9 y = 12$\\
(3) $6 x - 9 y = 20$\\
(4) $9 x - 9 y = 32$

Paper Questions

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