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

A(p, q) and B(r, s)

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) = (p, q) & (x₂, y₂) = (r, s)

We get:

(x - p)(x - r) + (y - q)(y - s) = 0

⇒ x² - rx - px + pr + y² - sy - qy + qs = 0

⇒ x² + y² - (r + p)x - (s + q)y + (pr + qs) = 0

Ans: x² + y² - (r + p)x - (s + q)y + (pr + qs) = 0