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

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Question: Find 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.

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

Find 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, which is (x - h)² + (y - k)² = r².
Step 4: Substitute h, k, and r into the equation. Replace h with 2, k with -3, and r with 5.
Step 5: The equation becomes (x - 2)² + (y - (-3))² = 5².
Step 6: Simplify the equation. Since y - (-3) is the same as y + 3, the equation is (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.
Substitution – Correctly substituting the center coordinates and radius into the equation is crucial for accuracy.