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Chapter 1: Problem 72

Write the standard form of the equation of the circle with the given characteristics. Center: \((-7,-4) ;\) Radius: 7

Short Answer

Expert verified
The equation of the circle in standard form is \((x+7)^2 + (y+4)^2 = 49\).

Step by step solution

01

Define the Variables

In this circumstance, the center of the circle is given by (-7, -4) and the radius is 7. As a result, our variables are \(h = -7\), \(k = -4\), and \(r = 7\).
02

Substitute the Variables into Equation

Using the formula for a circle's standard equation \((x-h)^2 + (y-k)^2 = r^2\), replace \(h\), \(k\), and \(r\) with -7, -4, and 7 respectively, we get \((x+7)^2 + (y+4)^2 = 7^2\).
03

Simplify the Equation

Finally, simplify the radius squared \(7^2\) to obtain 49. Thus, the standard form of the circle's equation is \((x+7)^2 + (y+4)^2 = 49\).

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