Let x = 2t, y = (t²)/3 be a conic. Let S be the focus and B be the point on the axis of the conic such that SA BA, where A is any point on the conic. If k is the ordinate of the centroid of the Δ SAB, then lim t → 1 k is equal to:

Coordinate Geometry: JEE Main 2022 Mathematics question

JEE Main 2022 · 25 Jun, Morning shift · Q4731

JEE Main 202225 Jun, Morning shiftMathematicsMediumCoordinate Geometry478× since 2002

Let

x = 2t

y = {{{t^2}} \over 3}

be a conic. Let S be the focus and B be the point on the axis of the conic such that

SA \bot BA

, where A is any point on the conic. If k is the ordinate of the centroid of the

\Delta

SAB, then

\mathop {\lim }\limits_{t \to 1} k

is equal to :