Answer:
[tex](x-230)^2+(y-220)^2=6100[/tex]
Step-by-step explanation:
The equation for a circle is [tex](x-h)^2+(y-k)^2=r^2[/tex], where [tex](h,k)[/tex] is the vertex of the circle and [tex]r[/tex] is the radius. Immediately, since the center of the circle is given, we know what [tex]h[/tex] and [tex]k[/tex] are. [tex]h[/tex] is 230 and [tex]k[/tex] is 220.
The only thing we need to find is the radius, which will just be the distance from the center (230,220) to a point on the circumference (170,170). The distance between them can be calculated using the distance formula, which is really just the Pythagorean Theorem rearranged. The formula states that [tex]d=\sqrt{x^2+y^2}[/tex], where [tex]x[/tex] is the change in the x-coordinates of the two points and [tex]y[/tex] is the change in the y-coordinates of the two points. Plug-in [tex]x[/tex] for 60 and [tex]y[/tex] for 50 to get [tex]d=\sqrt{50^2+60^2}[/tex]. Solve for [tex]d[/tex], arriving at [tex]\sqrt{6100}[/tex]. Therefore, the radius of the circle is [tex]\sqrt{6100}[/tex].
Finally, we have all of the components to create the equation of the circle. Plug-in 230 for [tex]h[/tex], 220 for [tex]k[/tex], and [tex]\sqrt{6100}[/tex] for [tex]r[/tex].
The equation of the circle will be [tex](x-230)^2+(y-220)^2=6100[/tex].
Hope this helps :)
