The standard equation of a circle is given by (x-h)² + (y-k)² = r², where (h,k) represents the coordinates of the center of the circle and r represents its radius.

Find the equation of the circle with centre (-3,2) and radius 6.

Answer: The equation of the circle is $(x+3)^2 + (y-2)^2 = 36$ .

Step-by-step solution

Step 1: Recall the standard equation of a circle

The standard equation of a circle is given by $(x-h)^2 + (y-k)^2 = r^2$ , where $(h,k)$ represents the coordinates of the center of the circle and $r$ represents its radius.

Step 2: Identify the given values

From the problem statement, we are given that the center of the circle is $(-3{,}2)$ and the radius is $6$ . Therefore, we can identify $h = -3$ , $k = 2$ , and $r = 6$ .

Step 3: Substitute the values into the equation

Now, substitute the identified values of $h$ , $k$ , and $r$ into the standard equation of the circle. This gives us $(x - (-3))^2 + (y - 2)^2 = 6^2$ .

Step 4: Simplify the equation

Simplify the expression. Subtracting a negative number is equivalent to adding a positive number, so $(x - (-3))$ becomes $(x+3)$ . Also, calculate $6^2$ , which is $36$ .

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