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What is the equation of a circle with center at (2, -3) and radius 5?
What is the equation of a circle with center at (2, -3) and radius 5?
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Q1
What is the equation of a circle with center at (2, -3) and radius 5?
(x - 2)² + (y + 3)² = 25
(x + 2)² + (y - 3)² = 25
(x - 2)² + (y - 3)² = 25
(x + 2)² + (y + 3)² = 25
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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.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the equation of a circle with center at (2, -3) and radius 5?
Solution:
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.
Steps: 6
Show Steps
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. So, r = 5.
Step 3: Use the standard form of the circle's equation: (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: Substitute r into the equation: (x - 2)² + (y + 3)² = 5².
Step 6: Calculate 5², which is 25. So, the equation becomes (x - 2)² + (y + 3)² = 25.
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