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 (-5,4) and radius 6.

Answer: $(x+5)^2 + (y-4)^2 = 36$

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 Given Values

From the problem statement, we are given that the center of the circle is $(-5{,}4)$ and the radius is $6$ . Therefore, we can identify $h = -5$ , $k = 4$ , and $r = 6$ .

Step 3: Substitute Values into the Equation

Now, substitute the identified values of $h$ , $k$ , and $r$ into the standard equation of the circle. This gives us $(x - (-5))^2 + (y - 4)^2 = 6^2$ .

Step 4: Simplify the Equation

Simplify the expression. Subtracting a negative number is equivalent to adding a positive number, so $(x - (-5))$ becomes $(x+5)$ . Also, calculate $6^2$ , which is $36$ .

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