Question

Regina is trying to sketch a circle on graph paper with the equation x2+y2−2x+22y+1=0 . Calculate where she would need to graph the center and radius of the circle by completing the square.

Answer 1

To sketch a circle with equation

x^2 + y^2 - 2x + 22y + 1 = 0,

we need to rewrite it in standard form:

(x - h)^2 + (y - k)^2 = r^2.

To do this, we first complete the square for x terms:

x^2 - 2x = (x - 1)^2 - 1,

and for y terms:

y^2 + 22y = (y + 11)^2 - 121.

Substitute these back into the equation:

(x - 1)^2 - 1 + (y + 11)^2 - 121 + 1 = 0,
(x - 1)^2 + (y + 11)^2 = 121.

Now we can see that the center is at (1, -11) and the radius is sqrt(121) = 11.

Thus, Regina should sketch the circle with center at (1, -11) and radius 11 on the graph paper.