Answer:
The equation of the circle can be written as:
- [tex]\left(x-4\right)^2+\left(y-4\right)^2=136[/tex]
Step-by-step explanation:
The general equation of a circle with center [tex](h,k)[/tex] and radius [tex]r[/tex] is:
[tex]\left(x-h\right)^2+\left(y-k\right)^2=r^2[/tex]
In our example, we know [tex]\left(h,k\right)=\left(4,4\right)[/tex], as we just have to make sure we need determine [tex]\:r^2[/tex].
[tex]\left(x-4\right)^2+\left(y-4\right)^2=r^2\:\:[/tex]
As the circle passes through (10, 14), that pair of values for x and y must satisfy the equation. So we have:
[tex]\left(10-4\right)^2+\left(14-4\right)^2=r^2[/tex]
[tex]\mathrm{Switch\:sides}[/tex]
[tex]r^2=\left(10-4\right)^2+\left(14-4\right)^2[/tex]
[tex]r^2=6^2+10^2[/tex]
[tex]r^2=36+100[/tex]
[tex]r^2=136[/tex]
Thus the equation of the circle can be written as:
[tex]\left(x-4\right)^2+\left(y-4\right)^2=136[/tex]
