The standard form for the equation of a circle is:
(x−h)2+(y−k)2=r2
Substitute (y−0)2 for y2
x2+14x+(y−0)2=0
Using the pattern (x−h)2=x2−2hx+h2, we observe that we must begin the process of completing the square by adding h2 to both sides:
x2+14x+h2+(y−0)2=h2
For this circle, the h2 term is, also the r2 term, because the we will soon find that the center is offset to the left the same distance as the radius.
We can find the value h by setting the right side of the pattern equal to the first 3 terms in the equation:
x2−2hx+h2=x2+14x+h2
The square terms cancel:
−2hx=14x
#h = -7 and h^2 = 49
Substitute (x−−7)2 for the corresponding terms on the left and
(x−−7)2+(y−0)2=49
The radius should be represented as a positive number squared.
(x−−7)2+(y−0)2=72
The center is found by observation (−7,2)
