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Chapter 2: Problem 38

Write the standard form of the equation of the circle with the given center and radius. $$\text { Center }(-5,-3), r=\sqrt{5}$$

Short Answer

Expert verified
The standard form of the equation of the circle with the given center (-5,-3) and radius \(\sqrt{5}\) is \( (x+5)^2 + (y+3)^2 = 5 \).

Step by step solution

01

Identify the Given Values

The center of the circle is given as (-5, -3) and the radius is given as \(\sqrt{5}\). These will substitute the (a, b) and r respectively in the standard form of the circle's equation.
02

Substitute the Values into the Equation of the Circle

Substitute the center (-5, -3) into the equation of the circle such that a=-5 and b=-3. Also substitute the radius, r = \(\sqrt{5}\). The standard form of the circle's equation is: \( (x-(-5))^2 + (y-(-3))^2 = (\sqrt{5})^2 \)
03

Simplify the Equation

Upon simplification, we get \( (x+5)^2 + (y+3)^2 = 5 \).

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