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Chapter 2: Problem 37

Write the standard form of the equation of the circle with the given center and radius. $$\text { Center }(-3,-1), r=\sqrt{3}$$

Short Answer

Expert verified
The standard form of the equation of the circle with center (-3,-1) and radius \(\sqrt{3}\) is \((x+3)^2 + (y+1)^2 = 3\).

Step by step solution

01

Identify the given values

In this problem, the center of the circle is \((-3,-1)\), which means \( h = -3\) and \(k = -1\). The radius of the circle is given as \(r = \sqrt{3}\), and we need to square that to get \(r^2 = 3\).
02

Substitute the values into the equation

We substitute the values of \(h, k, r^2\) into the standard form equation of a circle which is \((x-h)^2 + (y-k)^2 = r^2\), to get our circle equation \((x+3)^2 + (y+1)^2 = 3\).

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