Answer:
The equation that represents the circle is [tex](x-14)^{2}[/tex] + [tex](y-9)^{2}[/tex] = 13
Step-by-step explanation:
Given the center of circle (14,9) passes through point (16,12)
We know that the equation of circle is
[tex](x-h)^{2}[/tex] + [tex](y-k)^{2}[/tex] = [tex]r^{2}[/tex]
where (x,y) is any point on the circle, (h,k) is center of the circle and r is radius of circle.
From given data (x,y) is (16,12) and (h,k) is (14,9). Substituting these values in equation of circle, we get
[tex](16-14)^{2}[/tex] + [tex](12-9)^{2}[/tex] = [tex]r^{2}[/tex]
[tex]r^{2}[/tex] = [tex]2^{2}[/tex] + [tex]3^{2}[/tex]
[tex]r^{2}[/tex] = 13
Substituting the values of (h,K) and [tex]r^{2}[/tex] as (14,9) and 13 respectively in equation of circle, we get
[tex](x-14)^{2}[/tex] + [tex](y-9)^{2}[/tex] = 13
Hence the equation that represents the circle is [tex](x-14)^{2}[/tex] + [tex](y-9)^{2}[/tex] = 13
