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.

Simplify the expression. The term x-(-3) becomes x+3, and 7² becomes 49. Thus, the equation of the circle is (x+3)² + (y-8)² = 49.

Find the equation of the circle with centre (-3,8) and radius 7.

Answer: The equation of the circle is $(x+3)^2 + (y-8)^2 = 49$ .

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 $(-3{,}8)$ and the radius is $7$ . Therefore, we can identify $h=-3$ , $k=8$ , and $r=7$ .

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 $(x-(-3))^2 + (y-8)^2 = 7^2$ .

Step 4: Simplify the Equation

Simplify the expression. The term $x-(-3)$ becomes $x+3$ , and $7^2$ becomes $49$ . Thus, the equation of the circle is $(x+3)^2 + (y-8)^2 = 49$ .

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