Question 174571
First graph,
{{{x^2 + y^2 <= 1}}}
That's a circle centered at (0,0) with a radius of 1.
Including all of the interior points.
{{{drawing( 300, 300, -3, 3, -3, 3,grid(1),circle(0,0,.1),circle(0,0,.2),circle(0,0,.3),
circle(0,0,.4),
circle(0,0,.5),
circle(0,0,.6),
circle(0,0,.7),
circle(0,0,.8),
circle(0,0,.9),
circle( 0, 0, 1 ))}}}
Next graph,
{{{(x-1)^2 + y^2 <= 1}}}
That's a circle centered at (1,0) with a radius of 1.
Including all of the interior points.
{{{drawing( 300, 300, -3, 3, -3, 3,grid(1),circle(1,0,.1),circle(1,0,.2),circle(1,0,.3),
circle(1,0,.4),
circle(1,0,.5),
circle(1,0,.6),
circle(1,0,.7),
circle(1,0,.8),
circle(1,0,.9),circle(1,0,1))}}}
When you put those two together,
the region that satisfies both equations is the football shaped section in between the two circles.
{{{drawing( 300, 300, -3, 3, -3, 3,
green(line(.5,.75,.5,-.75)),
green(line(.35,.55,.35,-.55)),
green(line(.2,.35,.2,-.35)),
green(line(.1,.2,.1,-.2)),
green(line(.65,.55,.65,-.55)),
green(line(.8,.35,.8,-.35)),
green(line(.9,.2,.9,-.2)),
grid(1),circle(0,0,1),circle(1,0,1))}}}