Question

find an equation of the circle centered at (x, y) = (-1, 6) with a radius of r = 9 units.
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1. -/5 points

this question has several parts that must be completed sequentially. if you skip a part of the question, you will not receive any points for the skipped part.
tutorial exercise
use the method of completing the square to write an equation of the circle in standard form.
x^2 + y^2 - 14x - 4y + 47 = 0

Explanation:

Step1: Recall circle - equation formula

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

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

Given that the center \((h,k)=(-1,6)\) and \(r = 9\).

Step3: Substitute the values into the formula

Substitute \(h=-1\), \(k = 6\), and \(r = 9\) into the formula \((x - h)^2+(y - k)^2=r^2\). We get \((x-(-1))^2+(y - 6)^2=9^2\), which simplifies to \((x + 1)^2+(y - 6)^2=81\).

Answer:

\((x + 1)^2+(y - 6)^2=81\)