Question

assignment 10.0: distance and midpoint formulas; circles
score: 52/100 answered: 7/12
question 8
write the equation of the circle centered at (-4,5) with diameter 18.
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Explanation:

Step1: Find the radius

The radius \(r\) of a circle is half of the diameter. Given diameter \(d = 18\), then \(r=\frac{d}{2}=\frac{18}{2}=9\).

Step2: Recall the standard form of the circle equation

The standard form of the equation of a circle with center \((h,k)\) and radius \(r\) is \((x - h)^2+(y - k)^2=r^2\). Here, \(h=-4\), \(k = 5\), and \(r = 9\).

Step3: Substitute the values into the standard form

Substitute \(h=-4\), \(k = 5\), and \(r = 9\) into \((x - h)^2+(y - k)^2=r^2\). We get \((x-(-4))^2+(y - 5)^2=9^2\), which simplifies to \((x + 4)^2+(y - 5)^2=81\).

Answer:

\((x + 4)^2+(y - 5)^2=81\)