Question

The sides of a rectangle are given by the equations x = - 2, x = 4, y = - 2 and y = 5. Find the equation of the circle drawn on the diagonal of this rectangle as its diameter.

Answer 1

The intersection points in clockwise fashion are:( - 2, 5), (4, 5), (4, - 2), ( - 2, - 2). 

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) = ( - 2, 5) & (x₂, y₂) = (4, - 2)

We get:

(x + 2)(x - 4) + (y - 5)(y + 2) = 0 

⇒ x² - 4x + 2x - 8 + y² + 2y - 5y - 10 = 0 

⇒ x² + y² - 2x - 3y - 18 = 0

x² + y² - 2x - 3y - 18 = 0

x² + y² - 2x - 3y - 18 = 0