Question

Please help, I’ll mark your answer as brainliest!

Answer 1

Answer:

$(x-230)^2+(y-220)^2=6100$

Step-by-step explanation:

The equation for a circle is $(x-h)^2+(y-k)^2=r^2$, where $(h,k)$ is the vertex of the circle and $r$ is the radius. Immediately, since the center of the circle is given, we know what $h$ and $k$ are. $h$ is 230 and $k$ 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 $d=\sqrt{x^2+y^2}$, where $x$ is the change in the x-coordinates of the two points and $y$ is the change in the y-coordinates of the two points. Plug-in $x$ for 60 and $y$ for 50 to get $d=\sqrt{50^2+60^2}$. Solve for $d$, arriving at $\sqrt{6100}$. Therefore, the radius of the circle is $\sqrt{6100}$.

Finally, we have all of the components to create the equation of the circle. Plug-in 230 for $h$, 220 for $k$, and $\sqrt{6100}$ for $r$.

The equation of the circle will be $(x-230)^2+(y-220)^2=6100$.

Hope this helps :)