Question

On the coordinates plane XOY hatch a set of points whose coordinates satisfy the following inequalities in two variables x and y (show the boundary belonging to the set by a solid line and that not belonging to the set by a dash line).
$y⩾\sqrt{1-x^2},y+|x|⩽4$

Answer 1

R.E.F image

From inequality, $y\ge \sqrt{1-x^2}$ it is clean that $y\ge 0$

On squaring, $y^2=1-x^2\Rightarrow x^2+y^2=1$ which a represents a

circle with radius $=1$ unit & cost x $(0,0)$

As $y\ge 0$, it has origin above x-axis

inequality $y+|x|\le 4\Rightarrow y\le -|x|+4$

can be represented by lines $y=-x+4,y=x+4$

Test for origin

1) $y\ge \sqrt{1-x^2};$ Putting $(0,0)\Rightarrow 0\ge 1$ [false]

done not contain origin

2) $y+|x|\le 4;$ Putting $(0,0)\Rightarrow 0\le 4$ [True]

Region contain origin