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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.
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Practice Questions
1 question
Q1
Find the equation of the circle with center (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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Equation of circle: (x-h)² + (y-k)² = r² => (x-2)² + (y+3)² = 5².
Questions & Step-by-step Solutions
1 item
Q
Q: Find the equation of the circle with center (2, -3) and radius 5.
Solution:
Equation of circle: (x-h)² + (y-k)² = r² => (x-2)² + (y+3)² = 5².
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.
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.
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