What is the equation of a circle with center at (h, k) and radius r?

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Q: What is the equation of a circle with center at (h, k) and radius r?

Solution: The equation of a circle with center at (h, k) and radius r is (x - h)^2 + (y - k)^2 = r^2.

Steps: 6

Step 1: Identify the center of the circle, which is given as (h, k). This means 'h' is the x-coordinate and 'k' is the y-coordinate of the center.
Step 2: Identify the radius of the circle, which is given as 'r'. This is the distance from the center to any point on the circle.
Step 3: The general formula for the equation of a circle is based on the distance from the center to any point (x, y) on the circle.
Step 4: To express this mathematically, we use the formula: (x - h)^2 + (y - k)^2 = r^2.
Step 5: In this formula, (x - h) represents the horizontal distance from the center to the point (x, y), and (y - k) represents the vertical distance.
Step 6: Squaring these distances and adding them together gives us the equation of the circle.