Determine the equation of the circle with radius 4 and Centre (-2, 3).
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Step-by-Step Solution
Step 1: Recall the standard equation of a circle
The standard equation of a circle with center (h, k) and radius r is given by (x - h)^2 + (y - k)^2 = r^2$. This formula is derived from the distance formula, where every point (x, y) on the circle is at a fixed distance r from the center (h, k)$.
Step 2: Identify the given values
From the problem statement, we are given that the center of the circle is (-2, 3) and the radius is 4$. Therefore, we can identify h = -2$, k = 3$, and r = 4$.
Step 3: Substitute the values into the equation
Now, we substitute the identified values of h = -2$, k = 3$, and r = 4 into the standard equation of the circle. This gives us (x - (-2))^2 + (y - 3)^2 = 4^2$.
Step 4: Simplify the equation
Finally, we simplify the equation. Subtracting a negative number is equivalent to adding, so (x - (-2)) becomes (x + 2)$. Also, 4^2 simplifies to 16$. Thus, the equation of the circle is (x + 2)^2 + (y - 3)^2 = 16$.