Question

Find the equation of a circle with centre (2, 2) and passes through the point (4, 5).

Answer 1

Radius of circle = distance between centre (2, 2) and point (4, 5)

= `sqrt((2 - 4)^2 + (2 - 5)^2)`

= = `sqrt((2)^2 + (-3)^2)`

= `sqrt(4 + 9)`

= `sqrt13`

centre (2, 2) and radius = `sqrt13`

∴ Equation of circle,

= (x - h)² + (y - k)² = r²

= (x − 2)² + (y − 2)² = `(sqrt(13))^2`

= (x² − 4x + 4) + (y² − 4y − 4) = 13

= x² + y² − 4x − 4y − 5 = 0