Determine the equation of the circle with center (2, -3) and radius 5.

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Question: Determine the equation of the circle with center (2, -3) and radius 5.

Options:

Correct Answer: (x - 2)² + (y + 3)² = 25

Solution:

Equation of circle: (x - h)² + (y - k)² = r² => (x - 2)² + (y + 3)² = 5² = 25.

Determine the equation of the circle with center (2, -3) and radius 5.

Determine the equation of the circle with center (2, -3) and radius 5.

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

Circle Equation – The standard form of a circle's equation is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.