To write the equation of a circle, we can follow a simple formula that relates the center of the circle and its radius. The general equation of a circle with a center at the point (h, k) and radius r is given by the formula:
(x – h)² + (y – k)² = r²
In your case, the center of the circle is at the point (2, 3), which means:
- h = 2
- k = 3
The radius (r) is given as 4. Now, we need to substitute these values into the general equation:
Substituting h and k, we get:
(x – 2)² + (y – 3)² = 4²
Now, calculating the square of the radius:
(x – 2)² + (y – 3)² = 16
Thus, the equation of the circle with center (2, 3) and radius 4 is:
(x – 2)² + (y – 3)² = 16
This equation represents all the points (x, y) that are exactly 4 units away from the center point (2, 3).