Respuesta :
Answer:
The equation that represents circle C is [tex](x+2)^2+(y-10)^2=169[/tex].
Step-by-step explanation:
A circle is the set of all points in the plane which maintains a fixed finite distance r from a fixed point O = (a, b). Here O is called the center, and r is called the radius of that circle.
The standard equation for a circle with center (a, b) and radius r is
[tex](x-a)^2+(y-b)^2=r^2[/tex]
We are told that the center of this circle is (-2, 10), so
[tex](x+2)^2+(y-10)^2=r^2[/tex]
We are also told that the circle contains the point (10, 5), so we will use that information to find the radius r.
[tex](10+2)^2+(5-10)^2=r^2\\\\r^2=\left(10+2\right)^2+\left(5-10\right)^2\\\\r^2=12^2+5^2\\\\r^2=144+25\\\\r^2=169\\\\r=\sqrt{169}=13[/tex]
Therefore, the equation that represents circle C is
[tex](x+2)^2+(y-10)^2=13^2\\\\(x+2)^2+(y-10)^2=169[/tex]
