Question

Find the equation of the circle passing through the Points (4, 1)and (6, 5) and whose centre is on the line is 4x + y = 16​

Answer 1

Answer:

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Let say the equation be (x – h)² + (y – k)² = r²

Since the circle passes through points (4, 1) and (6, 5)

• (4 – h)² + (1 – k)² = r² ______[1]
• (6 – h)² + (5 – k)² = r²______[2]

Since the centre (h, k) of the circle lies on line 4x + y = 16

4h + k = 16 _______[3]

From equations (1) and (2), we obtain

(4 – h)² + (1 – k)² = (6 – h)² + (5 – k)²

16 – 8h + h² + 1 – 2k + k² = 36 – 12h + h² + 25 – 10k + k²

16 – 8h + 1 – 2k = 36 – 12h + 25 – 10k

4h + 8k = 44

h + 2k = 11 _______[4]

Find the equation of the circle passing through the Points (4, 1)and (6, 5) and whose centre is on the line is 4x + y = 16

Answer 2

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Let say the equation be (x – h)² + (y – k)² = r²

Since the circle passes through points (4, 1) and (6, 5)

(4 – h)² + (1 – k)² = r² ______[1]

(6 – h)² + (5 – k)² = r²______[2]

Since the centre (h, k) of the circle lies on line 4x + y = 16

4h + k = 16 _______[3]

From equations (1) and (2), we obtain

(4 – h)² + (1 – k)² = (6 – h)² + (5 – k)²

16 – 8h + h² + 1 – 2k + k² = 36 – 12h + h² + 25 – 10k + k²

16 – 8h + 1 – 2k = 36 – 12h + 25 – 10k

4h + 8k = 44

h + 2k = 11 _______[4]

Find the equation of the circle passing through the Points (4, 1)and (6, 5) and whose centre is on the line is 4x + y = 16