Find the equation of the circle passing through the points (0,2) (3,0)

1.	Find the equation of the circle passing through the points (0,2) (3,0) and (3,2).
Answer» Let equation of circle be x² + y² + 2gx + 2fy + c = 0 …. (1) Here circle passing through (0,2)(3,0) and (3,2) 6g + C = -9 …. (2) 4f + C = 4 …. (3) 6g + 4f + c = -13 …. (4) 6g – 4 = -13 6g = -9 g = \(\frac{-3}{2}\) 4f – 9 = 13 4f = -4 f = -1 - 4 + c = -4 c = 0 (1) ⇒ x² + y² – 6x – 2y = 0

Find the equation of the circle passing through the points (0,2) (3,0) and (3,2).

Answer»

Let equation of circle be

x² + y² + 2gx + 2fy + c = 0 …. (1)

Here circle passing through (0,2)(3,0) and (3,2)

6g + C = -9 …. (2)

4f + C = 4 …. (3)

6g + 4f + c = -13 …. (4)

6g – 4 = -13 6g = -9 g = \(\frac{-3}{2}\)

4f – 9 = 13

4f = -4 f = -1

- 4 + c = -4 c = 0 (1)

⇒ x² + y² – 6x – 2y = 0

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Find the equation of the circle passing through the points (0,2) (3,0) and (3,2).

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