Let x=2t,y=t^23 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…

Question

Let x=2t,y=t^23 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 limt→1k is equal to

MARKS Content Team · Accepted Answer

Correct answer: (D) 13/18. The parametric form x=2t,y=t^23 represents the parabola x^2=12y Given AS⊥AB So, m_AS·m_AB=-1 ⇒(3-t^23)/(0-2t)·(α-t^23)/(0-2t)=-1 ⇒3α=(27t^2+t^4)/(t^2-9) Ordinate of centroid of ΔSAB=k=(α+t^23+3)/3=(9+3α+t^2)/9 limt→1k=limt→11/99+t^2+(27t^2+t^4)/(t^2-9)=13/18

Let $x = 2 t, y = \frac{t^{2}}{3}$ be a conic. Let $S$ be the focus and $B$ be the point on the axis of the conic such that $S A ⊥ B A$ , where $A$ is any point on the conic. If $k$ is the ordinate of the centroid of the $Δ S A B$ , then $\lim_{t \to 1} k$ is equal to

Solution

Relevant Questions

Let x=2t,y=t23 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 limt→1k is equal to

Solution

Relevant Questions

Let $x = 2 t, y = \frac{t^{2}}{3}$ be a conic. Let $S$ be the focus and $B$ be the point on the axis of the conic such that $S A ⊥ B A$ , where $A$ is any point on the conic. If $k$ is the ordinate of the centroid of the $Δ S A B$ , then $\lim_{t \to 1} k$ is equal to