We simplify the equation. The term (x - (-3)) becomes (x + 3), and 8² simplifies to 64. This simplified form is the final equation of the circle.

Find the equation of the circle with centre (-3,2) and radius 8.

Answer: The equation of the circle is $(x + 3)^2 + (y - 2)^2 = 64$

Step-by-step solution

Step 1: Standard Equation of a Circle

The standard equation of a circle with center $(h, k)$ and radius $r$ is given by this formula. This formula is derived from the distance formula, representing all points $(x, y)$ that are a fixed distance $r$ from the center $(h, k)$ .

Step 2: Identify Given Values

From the problem statement, we are given that the center of the circle is $(-3, 2)$ and the radius is $8$ . We identify these values as $h = -3$ , $k = 2$ , and $r = 8$ .

Step 3: Substitute Values into the Equation

Now, we substitute the identified values of $h$ , $k$ , and $r$ into the standard equation of the circle. This step directly applies the given information to the general formula.

Step 4: Simplify the Equation

We simplify the equation. The term $(x - (-3))$ becomes $(x + 3)$ , and $8^2$ simplifies to $64$ . This simplified form is the final equation of the circle.

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