Question

A circle is described by the equation (x−1 2 ) 2 +(y−3 2 ) 2 =4 9 . What are the cordinates for the center of the circle and the length of the radius?

Answer 1

The explicit form of the equation of the circle, has the form:
\[(x- \alpha )^{2}+(y- \beta ) ^{2}=r ^{2}\]
Where alpha and beta are the coordinates of the center and r is the radius.
so if we are given:
\[(x-12)^{2}+(y-32)^{2}=49\]
We can observe it has the same structure, se we can find the values by saying:
\[ \alpha = 12\]
\[\beta = 32\]
\[r ^{2}=49\]