JEE Main 2026 · 4 Apr · Shift 2 · Mathematics Q24

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MathematicsInteger+4 / -1Question 24 of 75

Let A, B and C be the vertices of a variable right angled triangle inscribed in the parabola $y^2=16x$ . Let the vertex B containing the right angle be $(4,8)$ and the locus of the centroid of $\Delta ABC$ be a conic $C_0$ . Then three times the length of latus rectum of $C_0$ is ________.

Your answer

Answer and worked solution

Official answer: 16

Parametrise. Points $(4t^2,8t)$ ; B has $t=1$ . A chord between parameters $t_1,t_2$ has slope $\frac2{t_1+t_2}$ .

Right angle at B. $(a+1)(c+1)=-4$ . With $s=a+c$ , $p=ac$ : $p=-5-s$ .

Centroid. $X=\frac{4(1+a^2+c^2)}3=\frac{4s^2+8s+44}3$ and $Y=\frac{8(1+s)}3$ .

Eliminate s. $X=\frac{3Y^2}{16}+\frac{40}3$ , i.e. $Y^2=\frac{16}3\left(X-\frac{40}3\right)$ .

Latus rectum $\frac{16}3$ ; three times it is 16.

Answer: 16

Topics:Parabola Locus

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JEE Main 2026 · 4 Apr · Shift 2, Mathematics question 24