What is the equation of the circle with center (2, -3) and radius 5?
Correct Answer: (x-2)² + (y+3)² = 25
- Step 1: Identify the center of the circle, which is given as (h, k) = (2, -3).
- Step 2: Identify the radius of the circle, which is given as r = 5.
- Step 3: Write down the general equation of a circle: (x - h)² + (y - k)² = r².
- Step 4: Substitute h = 2 and k = -3 into the equation: (x - 2)² + (y - (-3))² = r².
- Step 5: Simplify the equation: (x - 2)² + (y + 3)² = r².
- Step 6: Calculate r²: Since r = 5, r² = 5² = 25.
- Step 7: Substitute r² into the equation: (x - 2)² + (y + 3)² = 25.
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