JEE Main 2022 · 25 Jun · Shift 1 · Mathematics Q19

← JEE Main 2022 · 25 Jun · Shift 1

MathematicsSingle correct+4 / -1Question 19 of 90

Let $x=2t$ , $y=\dfrac{t^2}3$ be a conic. Let S be the focus and B be the point on the axis of the conic such that $SA\perp BA$ , where A is any point on the conic. If k is the ordinate of the centroid of the $\Delta SAB$ , then $\displaystyle\lim_{t\to1}k$ is equal to :

\dfrac{17}{18}

\dfrac{19}{18}

\dfrac{11}{18}

\dfrac{13}{18}

Answer and worked solution

Official answer: D

Conic. $x^2=12y$ : focus $S(0,3)$ , axis the $y$ -axis.

At $t=1$ . $A=\left(2,\frac13\right)$ . With $B=(0,b)$ : $\overrightarrow{AS}\cdot\overrightarrow{AB}=0$ gives $4-\frac83\left(\frac13-b\right)=0$ , so $b=-\frac76$ .

Centroid ordinate. $k=\dfrac13\left(3+\dfrac13-\dfrac76\right)=\dfrac{13}{18}$ .

(D)

Topics:Parabola Distance and section formulae

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JEE Main 2022 · 25 Jun · Shift 1, Mathematics question 19