The parametric form x=2t,y=3t2 represents the parabola x2=12y
Given AS⊥AB
So, mAS⋅mAB=−1
⇒(0−2t)(3−3t2)⋅(0−2t)(α−3t2)=−1
⇒3α=t2−927t2+t4
Ordinate of centroid of ΔSAB=k=3α+3t2+3=99+3α+t2
t→1limk=t→1lim91(9+t2+(t2−9)27t2+t4)=1813
Let x=2t,y=3t2 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 ΔSAB, then t→1limk is equal to
Held on 25 Jun 2022 · Verified 6 Jul 2026.
1817
1819
1811
1813
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