Graph the circle (y−1)2+x2=1 by solving for y and graphing two equations involved.
(y−1)2+x2=1Model(y−1)2=1−x2Subtract x2y−1=±√1−x2Take the square rooty=1±√1−x2Add 1y=1+√1−x2 and y=1−√1−x2Solve for y
Thus, the circle is descended by the graphs of the equations
y=1+√1+x2 and y=1−√1−x2
The first equation represents the top half of the circle because y≥0 while the second represents the bottom half. If we graph the first equation in the viewing rectangle [−1,1] by [−2,2] then we get...
The graph of the second equation is....
Graphing the semicircles together on the same viewing screen, we get the full circle...
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