Tuesday, January 14, 2020

College Algebra, Chapter 2, 2.3, Section 2.3, Problem 28

Graph the circle (y1)2+x2=1 by solving for y and graphing two equations involved.

(y1)2+x2=1Model(y1)2=1x2Subtract x2y1=±1x2Take the square rooty=1±1x2Add 1y=1+1x2 and y=11x2Solve for y

Thus, the circle is descended by the graphs of the equations
y=1+1+x2 and y=11x2

The first equation represents the top half of the circle because y0 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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