We have given points `A(x_(1),y_(1))` and `B(x_(2),y_(2))` and its midpoint is C`((x_(1)+x_(2))/(2),(y_(1)_y_(2))/(2))`
(1) `x^(2)+2y^(2)le1` represents interior region of ellipse `x^(2)+2y^(2)le1` as shown in the given figure.
Clearly, for any two points A and B in the shaded region, mid point of AB also lies in the shaded region.
(2) Max `{|x|,|y|}le1`
`rArr" "|x|le1 and |y|le1`
`rArr" "-1lexle1 and -1leyle1`
This represents the interior region of a square with its sides
`x=pm1 and y=pm1` as shown in the given figure.
(3) `x^(2)-y^(2)le1`
represents the exterior region of hyperbola as shown in the given figure.
As shown in the figure for points A and B selected in the region, the midpoint does not necessarily lie in the same region.
(4) `y^(2)lex` represents interior region of the parabola `y^(2)=x` as shown in the given figure.
Clearly, for any two points A and B in the shaded region, mid point of AB also lies in the shaded region.
