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Question
Find the equation of the circle whose centre is (2, 3) and which passes through (1, 4).
Solution
Centre (h, k) = (2, 3)
Radius = `sqrt((1 - 2)^2 + (4 - 3)^2)`
`= sqrt((-1)^2 + 1^2)`
`= sqrt2`
Equation of the circle with centre (h, k) and radius r is (x – h)2 + (y – k)2 = r2
⇒ (x – 2)2 + (y – 3)2 = `(sqrt2)^2`
⇒ x2 – 4x + 4 + y2 – 6y + 9 = 2
⇒ x2 + y2 – 4x – 6y + 11 = 0
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