MHB Can I Graph a Semicircle By Hand?

[mathdad]

An equation of the circle is given below. Solve the equation for y, and then graph the resulting semicircle.

(x - 4)^2 + (y - 1)^2 = 9

I must isolate y. I get it. My question concerns graphing the semicircle by hand. Can it be graphed by hand or should I simply use the wolfram math site for graphing? If by hand, can you provide several points that would allow me to draw the semicircle correctly?

 

[MarkFL]

You know the center of the circle is $(4,1)$ amd the radius is $r=3$. So, this gives you 3 easy points (if you choose the "upper" semi-circle):

$(4+3,1)=(7,1))$

$(4,1+3)=(4,4)$

$(4-3,1)=(1,1)$

Then connect the 3 points with a circular arc.

 

[mathdad]

You know the center of the circle is $(4,1)$ amd the radius is $r=3$. So, this gives you 3 easy points (if you choose the "upper" semi-circle):

$(4+3,1)=(7,1))$

$(4,1+3)=(4,4)$

$(4-3,1)=(1,1)$

Then connect the 3 points with a circular arc.

Plotting the three points is easy but I am slightly confused in terms of how you came up with the points.

 

[MarkFL]

Plotting the three points is easy but I am slightly confused in terms of how you came up with the points.

The first point is 3 units to the right of the circle's center, the second point is 3 units up and the third point is 3 units to the left. :D

 

[mathdad]

The first point is 3 units to the right of the circle's center, the second point is 3 units up and the third point is 3 units to the left. :D

I totally get it. Thanks again.