Questions: Given a circle with center (-5,-2) and radius 1, (a) Write an equation of the circle in standard form. (b) Graph the circle. Part 1 of 2 (a) An equation of the circle in standard form is

Given a circle with center (-5,-2) and radius 1, (a) Write an equation of the circle in standard form. (b) Graph the circle.

Part 1 of 2 (a) An equation of the circle in standard form is

Transcript text: Given a circle with center $(-5,-2)$ and radius 1 , (a) Write an equation of the circle in standard form. (b) Graph the circle. Part 1 of 2 (a) An equation of the circle in standard form is $\square$

Solution

Solution Steps

Step 1: Identify the Center of the Circle

To find the equation of a circle, we first need to identify its center. The center of the circle is given as (-5, -2).

Step 2: Determine the Radius of the Circle

The next step is to determine the radius of the circle. The radius of the circle is given as 1.

Step 3: Substitute Values into the Standard Form Equation

Using the center (-5, -2) and radius 1, we substitute these values into the standard form equation of a circle: $(x - h)^2 + (y - k)^2 = r^2$. This gives us the equation: \[(x + 5)^2 + (y + 2)^2 = 1\].