Question

11.1: distance and midpoint formulas; circles
score: 4/24 answered: 4/18
question 5
write the equation of the circle centered at (7, -9) with diameter 20.
question help: video message instructor

Explanation:

Step1: Find the radius

The radius \(r\) of a circle is half of the diameter \(d\). Given \(d = 20\), then \(r=\frac{d}{2}=\frac{20}{2}=10\).

Step2: Use the standard form of the circle 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. Here, \(h = 7\), \(k=-9\) and \(r = 10\).
Substitute these values into the formula: \((x - 7)^2+(y-(-9))^2=10^2\).

Answer:

\((x - 7)^2+(y + 9)^2=100\)