Question

Find the equation of the circle whose centre is (2, 3) and which passes through (1, 4).

Answer 1

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