IIT-JEE 1981Question 1
Each of the four inequalities given below defines a region in the $xy$ plane. One of these four regions does not have the following property: for any two points $(x_1,y_1)$ and $(x_2,y_2)$ in the region, the point $\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$ is also in the region. The inequality defining this region is
Points and Straight Lines
Solution
(A) ellipse disc, (B) square, (D) region right of a parabola are convex. $x^2-y^2\le1$ is not: $(2,\sqrt3)$ and $(2,-\sqrt3)$ lie in it but their midpoint $(2,0)$ gives $4>1$.