Parametric Equations

Interactive Feed

Let $O$ be the vertex and $Q$ be any point on the parabola, $x^{2} = 8 y$ . If the point $P$ divides the line segment $O Q$ internally in the ratio $1 : 3$ , then locus of $P$ is:

y^{2} = 2 x

x^{2} = 2 y

x^{2} = y

y^{2} = x

JEE Main 2024 (09 Apr Shift 2)

LEVELJEE Advanced

Let $A, B$ and $C$ be three points on the parabola $y^{2} = 6 x$ and let the line segment $A B$ meet the line $L$ through $C$ parallel to the $x$ -axis at the point $D$ . Let $M$ and $N$ respectively be the feet of the perpendiculars from $A$ and $B$ on $L$ . Then $(\frac{A M \cdot B N}{C D})^{2}$ is equal to _________

JEE Main 2025 April

LEVELJEE Advanced

A line passing through the point $P (5, 5)$ intersects the ellipse $\frac{x ^{2}}{36} + \frac{y ^{2}}{25} = 1$ at $A$ and $B$ such that $(P A) \cdot (P B)$ is maximum. Then $5 (P A^{2} + P B^{2})$ is equal to :

JEE Main 2026 (21 January Shift 2)

Let one end of a focal chord of the parabola $y^{2} = 16 x$ be $(16, 16)$ . If $P (α, β)$ divides this focal chord internally in the ratio $5 : 2$ , then the minimum value of $α + β$ is equal to :