Problem 78 - College Algebra

Question

Give an example of a circle's equation in standard form. Describe how to find the center and radius for this circle.

Step-by-Step Solution

Answer

The standard form equation of a circle given in this example is \( (x - 3)^2 + (y - 5)^2 = 16 \). The center of the circle is at \( (3,5) \) and its radius is 4.

Step 1: Define circle's standard form equation

First, you need to understand that the standard form for the equation of a circle is \( (x - h)^2 + (y - k)^2 = r^2 \), where \( (h,k) \) are the coordinates of the center and \( r \) is the radius

Step 2: Give an example of a circle's equation in standard form

Let's consider a circle with the following standard form equation: \( (x - 3)^2 + (y - 5)^2 = 16 \)

Step 3: Identify circle's center and radius

From this equation, we can see that the center \( (h,k) \) is \( (3,5) \) because of the expressions \( (x - 3) \) and \( (y - 5) \). The radius \( r \) can be found by taking the square root of 16, so \( r = 4 \)