Question

write the equation of the circle centered at $(-10,10)$ with radius 8. enter your equation without a square root. question help: video

Explanation:

Step1: Recall the standard form of a circle's equation

The standard form of the equation of a circle is \((x - h)^2+(y - k)^2=r^2\), where \((h,k)\) is the center of the circle and \(r\) is the radius.

Step2: Identify the values of \(h\), \(k\), and \(r\)

Given that the center \((h,k)=(- 10,10)\) and radius \(r = 8\).

Step3: Substitute the values into the standard form

Substitute \(h=-10\), \(k = 10\), and \(r = 8\) into \((x - h)^2+(y - k)^2=r^2\).
We get \((x-(-10))^2+(y - 10)^2=8^2\).
Simplify it to \((x + 10)^2+(y - 10)^2=64\).

Answer:

\((x + 10)^2+(y - 10)^2=64\)