Write the equation of a circle with center A (3; 4) passing through point B (5; 2).
| August 3, 2021 | education
The equation of the circle is (x – x0) ² + (y – y0) ² = R², where x0 and y0 are the coordinates of the center of the circle, and R is the radius of the circle.
Since the center of the circle is at point A (3; 4), the coordinates are x0 = 3, y0 = 4.
The radius of the circle is equal to the distance from the center of the circle to any point on the circle, that is, the radius is equal to the length of the segment AB.
A (3; 4), B (5; 2).
AB = √ ((3 – 5) ² + (4 – 2) ²) = √ (4 + 4) = √8.
Hence, the equation of the circle will be equal to (x – 3) ² + (y – 4) ² = (√8) ².
Answer: (x – 3) ² + (y – 4) ² = 8.
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