CAT (QA) PYQs

Let $ABCD$ be a parallelogram such that the coordinates of its three vertices $A, B, C$ are $(1, 1), (3, 4)$ and $(-2, 8)$, respectively. Then, the coordinates of the vertex $D$ are

If three sides of a rectangular park have a total length $400 \mathrm{ft}$, then the area of the park is maximum when the length (in ft ) of its longer side is

A quadrilateral $A B C D$ is inscribed in a circle such that $A B: C D=2: 1$ and $B C: A D=5: 4$. If $A C$ and $B D$ intersect at the point $E$, then $A E$ : $C E$ equals