Answer:
The equation that represents the circle is
+
= 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
+
= ![r^{2}](https://tex.z-dn.net/?f=r%5E%7B2%7D)
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
+
= ![r^{2}](https://tex.z-dn.net/?f=r%5E%7B2%7D)
=
+ ![3^{2}](https://tex.z-dn.net/?f=3%5E%7B2%7D)
= 13
Substituting the values of (h,K) and
as (14,9) and 13 respectively in equation of circle, we get
+
= 13
Hence the equation that represents the circle is
+
= 13