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 its diameter.

Answer 1

The given equation of the sides are x = −2, x = 4, y = −2, y = 5

∴ The ends of any one of the diameter are A(−2, −2) and B(4, 5). 

We know equation of a circle with (x₁,y₁), (x₂, y₂ ) as the two ends of any of its diameter is

(x − x₁ )(x − x₂ ) + (y− y₁ )(y − y₂ ) = 0      (1)

 So, let (x₁, y₁ ) = (−2, −2) and (x₂, y₂ ) = (4, 5).

 (1) ⇒ (x + 2)(x − 4) + (y + 2)(y− 5) = 0 

⇒ x² − 2x − 8 + y² − 3y − 10 = 0 

⇒ x² + y² − 2x − 3y − 18 = 0, is the required equation of the circle.