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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
Thus, the standard form of the equation of the circle with the given center and radius is \((x+7)^2 + (y+4)^2 = 49\).

Step by step solution

01

Identify the Center and Radius

From the exercise, it can be determined that the center (h, k) of the circle is (-7, -4). So, h = -7 and k = -4. Furthermore, radius r is given as 7.
02

Substitute Center and Radius into Standard Form Equation

Use the values of h, k and r to substitute into the standard form of equation of a circle \((x-h)^2 + (y-k)^2 = r^2\). The equation then becomes \((x-(-7))^2 + (y-(-4))^2 = 7^2\).
03

Simplify the Equation

Simplify the equation, ending up with \((x+7)^2 + (y+4)^2 = 49\).

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