Question

Find the equation of the circle, the coordinates of the end points of one of whose diameters are

Answer 1

The equation of a circle passing through the coordinates of the end points of diameters is:

(x - x₁) (x - x₂) + (y - y₁)(y - y₂) = 0

Substituting, values:(x₁, y₁) = (3, 2) & (x₂, y₂) = (2, 5) 

We get: 

(x - 3)(x - 2) + (y - 2)(y - 5) = 0 

⇒ x² - 2x - 3x + 6 + y² - 5y - 2y + 10 = 0 

⇒ x² + y² - 5x - 7y + 16 = 0 

x² + y² - 5x - 7y + 16 = 0